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How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 1, -1, 2, -2, 3?

Answer 1

Lily Anderson

#f(x) = x^5-3x^4-5x^3+15x^2+4x-12#

Each zero #a# corresponds to a linear factor #(x-a)#, so we can write:

#f(x) = (x-1)(x+1)(x-2)(x+2)(x-3)#

#=(x^2-1)(x^2-4)(x-3)#

#=(x^4-5x^2+4)(x-3)#

#=x^5-3x^4-5x^3+15x^2+4x-12#

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Answer 2

Lincoln Anderson

To write a polynomial function of least degree and leading coefficient 1 with the given zeros, you can use the factored form of a polynomial equation. The factored form is obtained by writing the polynomial as a product of linear factors corresponding to its zeros.

The given zeros are 1, -1, 2, -2, and 3.

To write the polynomial function, we use these zeros to form the factors:

(x - 1)(x + 1)(x - 2)(x + 2)(x - 3)

Expanding this expression gives the polynomial function:

f(x) = (x - 1)(x + 1)(x - 2)(x + 2)(x - 3)

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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.