How do you use the Intermediate Value Theorem to show that the polynomial function #f(x) = x^4 + 8x^3 - x^2 + 2# has a zero in the interval [-1, 1]?

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x^2 + 2 ) has a zero in the interval ([-1, 1]), we need toTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changesTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to showTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes signTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign overTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign withinTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over thatTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within thatTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that intervalTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that intervalTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

FirstTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluateTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

FirstTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) )To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) andTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) )To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) andTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 +To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

SinceTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

SinceTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 )To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) andTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 )To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) andTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ),To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), andTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and theTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ),To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the functionTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and theTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function isTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the functionTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuousTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 andTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 andTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by theTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, byTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate ValueTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by theTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value TheTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate ValueTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value TheTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, thereTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value TheoremTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there existsTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists aTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, thereTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a valueTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists atTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( cTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at leastTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) inTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( cTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in theTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c )To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) inTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]\To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1])To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]\To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) suchTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1])To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such thatTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) suchTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such thatTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that (To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(cTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( fTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(cTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c)To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) =To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial functionTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function hasTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has aTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 \To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zeroTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ).To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero inTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). ThusTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in theTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero inTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the intervalTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the intervalTo use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the interval ([-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the interval ([-To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the interval ([-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the interval ([-1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the interval ([-1, To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the interval ([-1,To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the interval ([-1, 1To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the interval ([-1, To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the interval ([-1, 1]\To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the interval ([-1, 1]\To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the interval ([-1, 1]).To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the interval ([-1, 1]).To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), we need to show that the function changes sign over that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = 1^4 + 8(1)^3 - 1^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists a value ( c ) in the interval ([-1, 1]) such that ( f(c) = 0 ). Therefore, the polynomial function has a zero in the interval ([-1, 1]).To use the Intermediate Value Theorem to show that the polynomial function ( f(x) = x^4 + 8x^3 - x^2 + 2 ) has a zero in the interval ([-1, 1]), you need to demonstrate that the function changes sign within that interval.

First, evaluate ( f(-1) ) and ( f(1) ).

( f(-1) = (-1)^4 + 8(-1)^3 - (-1)^2 + 2 = 1 - 8 - 1 + 2 = -6 )

( f(1) = (1)^4 + 8(1)^3 - (1)^2 + 2 = 1 + 8 - 1 + 2 = 10 )

Since ( f(-1) = -6 ) and ( f(1) = 10 ), and the function is continuous between -1 and 1, by the Intermediate Value Theorem, there exists at least one ( c ) in ([-1, 1]) such that ( f(c) = 0 ). Thus, the polynomial function has a zero in the interval ([-1, 1]).