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

Apr 16, 2016

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

#### Explanation:

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

$\left(x - 3\right)$, $\left(x + 2\right)$, $x$ and $\left(x - 2\right)$.

We get the polynomial by multiplying them. Hence polynomial is

x(x-3)(x+2)(x-2)=(x^2-3x)((x^2-4)=x^4-3x^3-4x^2+12x