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

Jun 9, 2016

${x}^{4} + 3 {x}^{3} - 4 {x}^{2} - 12 x$

#### Explanation:

The standard form of a polynomial is when the polynomial is written as a sum of decreasing power of the variable, in this case $x$. The question has given us the information to write the factored version of the polynomial where it has been set equal to zero, i.e.:

$\left(x + 3\right) \left(x + 2\right) \left(x\right) \left(x - 2\right) = 0$

To get our polynomial in standard form, we need to multiply the factors out.

$\left({x}^{2} + 5 x + 6\right) \left(x\right) \left(x - 2\right) = 0$

$\left({x}^{3} + 5 {x}^{2} + 6 x\right) \left(x - 2\right) = 0$

${x}^{4} + 3 {x}^{3} - 4 {x}^{2} - 12 x = 0$

so the standard form for our polynomial is

${x}^{4} + 3 {x}^{3} - 4 {x}^{2} - 12 x$