# How do you write a polynomial function in standard form given the roots x=-3,0,0,5?

Jun 10, 2017

${x}^{4} - 2 {x}^{3} - 15 {x}^{2}$

#### Explanation:

$\text{ given the roots then the factors of the polynomial will be}$

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

$\textcolor{w h i t e}{y} = {x}^{2} \left({x}^{2} - 2 x - 15\right)$

$\textcolor{w h i t e}{y} = {x}^{4} - 2 {x}^{3} - 15 {x}^{2} \leftarrow \textcolor{red}{\text{ in standard form}}$