# How do you write a polynomial function in standard form with zeros at -6, 2, and 5?

Aug 2, 2018

${x}^{3} - {x}^{2} - 32 x + 60$

#### Explanation:

If $\alpha , \beta$ and $\gamma$ are the zeros,

the polynomial function is $\left(x - \alpha\right) \left(x - \beta\right) \left(x - \gamma\right)$

Hence, for zeros $- 6 , 2$ and $5$ polynomial function is

$\left(x - \left(- 6\right)\right) \left(x - 2\right) \left(x - 5\right)$

= $\left(x + 6\right) \left({x}^{2} - 5 x - 2 x + 10\right)$

= $\left(x + 6\right) \left({x}^{2} - 7 x + 10\right)$

= ${x}^{3} - 7 {x}^{2} + 10 x + 6 {x}^{2} - 42 x + 60$

= ${x}^{3} - {x}^{2} - 32 x + 60$