# How do you find a polynomial function that has zeros -2, -1, 0, 1, 2?

Jan 12, 2017

${x}^{5} - 5 {x}^{3} + 4 x$

#### Explanation:

The polynomial function would consist of factors $\left(x + 2\right) \left(x + 1\right) x \left(x - 1\right) \left(x - 2\right)$

On simplification it would be $x \left({x}^{2} - 1\right) \left({x}^{2} - 4\right)$

Or, $x \left({x}^{4} - 5 {x}^{2} + 4\right)$

Or ${x}^{5} - 5 {x}^{3} + 4 x$