How do you write a polynomial in standard form given zeros 3, 2, -1?

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How do you write a polynomial in standard form given zeros 3, 2, -1?

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Answer 1 · 2016-03-05T00:25:40

$x^{3} - 4 x^{2} + x + 6$ $x^3-4x^2+x+6$

Explanation:

Using the fact that if $(x - a)$ $(x-a)$ is a factor of a polynomial, then $a$ $a$ is a root of that polynomial, we can generate a polynomial with a given set of roots easily by starting from its factored form.

In this case, given the roots $3$ $3$ , $2$ $2$ , and $- 1$ $-1$ , we would have

$P (x) = (x - 3) (x - 2) (x - (- 1)) = x^{3} - 4 x^{2} + x + 6$ $P(x) = (x-3)(x-2)(x-(-1)) = x^3-4x^2+x+6$

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How do you write a polynomial in standard form given zeros 3, 2, -1?

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