# How do you write a polynomial function in standard form with the given zeros: -1, 3, 5?

The simplest such (non-zero) polynomial is:

#f(x) =x^3-7x^2+7x+15#

As a product of linear factors, we can define:

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To write a polynomial function in standard form with the given zeros -1, 3, and 5, you use the factored form of the polynomial and multiply the factors together. The factored form of the polynomial is given by:

[ f(x) = (x - (-1))(x - 3)(x - 5) ]

Now, you expand and simplify this expression to obtain the polynomial in standard form:

[ f(x) = (x + 1)(x - 3)(x - 5) ]

[ f(x) = (x^2 - 3x + x - 3)(x - 5) ]

[ f(x) = (x^2 - 2x - 3)(x - 5) ]

[ f(x) = x^3 - 5x^2 - 2x^2 + 10x - 3x + 15 ]

[ f(x) = x^3 - 7x^2 + 7x + 15 ]

So, the polynomial function in standard form with the given zeros is ( f(x) = x^3 - 7x^2 + 7x + 15 ).

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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.

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.

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.

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- If one of the roots of #x^3-3x+1=0# is given by the rational (companion) matrix #((0,0,-1),(1,0,3),(0,1,0))#, then what rational(?) matrices represent the other two roots?

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