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How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3, -3, 1?

Answer 1

Elias Ackerman

#color(green)(f(x)=x^3-x^2-9x+9)#

If the polynomial has zeros at #3, -3, and 1# then it has factors: #color(white)("XXX")(x-3), (x+3), and (x-1)#

As a minimal degree polynomial (with leading coefficient #1#) #color(white)("XXX")(x-3) * (x+3) * (x-1)#

#color(white)("XXX")=(x^2-9) * (x-1)#

#color(white)("XXX")=x^3-x^2-9x+9#

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Answer 2

Lincoln Anderson

To write a polynomial function of least degree and leading coefficient 1 with zeros at 3, -3, and 1, we use the factored form of a polynomial. Since the zeros are given, we can write the polynomial as:

[ f(x) = (x - 3)(x + 3)(x - 1) ]

Expanding this expression gives:

[ f(x) = (x^2 - 9)(x - 1) ]

[ f(x) = x^3 - x^2 - 9x + 9 ]

So, the polynomial function of least degree and leading coefficient 1 with zeros at 3, -3, and 1 is ( f(x) = x^3 - x^2 - 9x + 9 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.