# How do you write a polynomial in standard form given zeros 4, sqrt(5) and -sqrt(5)?

Mar 9, 2016

#### Answer:

${x}^{3} - 4 {x}^{2} - 5 x + 20$

#### Explanation:

The polynomial with zeros: $4 , \sqrt{5}$ and $- \sqrt{5}$ is

$\left(x - 4\right) \left(x - \sqrt{5}\right) \left(x + \sqrt{5}\right)$ or

$\left(x - 4\right) \left({x}^{2} - 5\right)$ (using $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$)

= $x \left({x}^{2} - 5\right) - 4 \left({x}^{2} - 5\right)$

= ${x}^{3} - 5 x - 4 {x}^{2} + 20$

= ${x}^{3} - 4 {x}^{2} - 5 x + 20$