# How do you find a polynomial function that has zeros 4, -3, 3, 0?

Mar 9, 2017

$f \left(x\right) = {x}^{4} - 4 {x}^{3} - 9 {x}^{2} + 36 x$

#### Explanation:

If $f \left(x\right)$ has zeros of $4 , - 3 , 3 , 0 \to \left(x - 4\right) , \left(x + 3\right) , \left(x - 3\right) , x$ are factors of $f \left(x\right)$

Hence: $f \left(x\right) = \left(x - 4\right) \left(x + 3\right) \left(x - 3\right) x$

$f \left(x\right) = x \left(x - 4\right) \left({x}^{2} - 9\right)$

$= \left({x}^{2} - 4 x\right) \left({x}^{2} - 9\right)$

$= {x}^{4} - 4 {x}^{3} - 9 {x}^{2} + 36 x$