# How do you write a polynomial function given the real zeroes -5,2,-2 and coefficient 1?

Nov 13, 2015

$f \left(x\right) = {x}^{3} + 5 {x}^{2} - 4 x - 20$

#### Explanation:

$\left(x + 5\right) \left(x - 2\right) \left(x + 2\right) = 0$ if $x \in \left\{- 5 , 2 , - 2\right\}$
$\textcolor{w h i t e}{\text{XXX}}$Since for any value of $x$ in this set
$\textcolor{w h i t e}{\text{XXX}}$one of the terms will be $= 0$

$\left(x + 5\right) \left(x - 2\right) \left(x + 2\right)$
$\textcolor{w h i t e}{\text{XXX}} = \left(x + 5\right) \left({x}^{2} - 4\right)$
$\textcolor{w h i t e}{\text{XXX}} = {x}^{2} + 5 {x}^{2} - 4 x - 20$

(I assume when the questions says "coefficient 1" it means the coefficient of the highest order term).