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How do you write a polynomial in standard form given the zeros x=-3,-2,0,2?

1 Answer

Shwetank Mauria

Apr 16, 2016

The polynomial is $x^{4} - 3 x^{3} - 4 x^{2} + 12 x$ $x^4-3x^3-4x^2+12x$

Explanation:

If zeros of the polynomial are $3, - 2, 0, 2$ $3, -2, 0, 2$ , the factors of polynomial are

$(x - 3)$ $(x-3)$ , $(x + 2)$ $(x+2)$ , $x$ $x$ and $(x - 2)$ $(x-2)$ .

We get the polynomial by multiplying them. Hence polynomial is

$x (x - 3) (x + 2) (x - 2) = (x^{2} - 3 x) ((x^{2} - 4) = x^{4} - 3 x^{3} - 4 x^{2} + 12 x$ $x(x-3)(x+2)(x-2)=(x^2-3x)((x^2-4)=x^4-3x^3-4x^2+12x$

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