# How do you find a polynomial function that has zeros x=-3, 0, 1 and degree n=3?

Jun 25, 2017

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

#### Explanation:

$\text{given zeros } x = - 3 , x = 0 , x = 1$

$\text{then factors are } \left(x + 3\right) , \left(x - 0\right) , \left(x - 1\right)$

$\Rightarrow f \left(x\right) = x \left(x + 3\right) \left(x - 1\right)$

$\textcolor{w h i t e}{\Rightarrow f \left(x\right)} = x \left({x}^{2} + 2 x - 3\right)$

$\textcolor{w h i t e}{\Rightarrow f \left(x\right)} = {x}^{3} + 2 {x}^{2} - 3 x \leftarrow \text{ is a possible function}$
graph{x^3+2x^2-3x [-10, 10, -5, 5]}