# How do you factor x^3 -3x-2=0?

Apr 7, 2016

${x}^{3} - 3 x - 2 = \textcolor{g r e e n}{\left(x + 1\right) \left(x + 1\right) \left(x - 2\right)}$

#### Explanation:

Given:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{1} {x}^{3} - \textcolor{b l u e}{3} x - \textcolor{red}{2}$
Note that $\textcolor{red}{- 1 - 2} = \textcolor{b l u e}{- 3}$
which implies $x = - 1$ is a solution to the given equation
and therefore
$\textcolor{w h i t e}{\text{XXX}} \left(x + 1\right)$ is a factor of the expression:

$\left({x}^{3} - 3 x - 2\right) \div \left(x + 1\right) = \left({x}^{2} - x - 2\right)$
$\textcolor{w h i t e}{\text{XXX}}$use polynomial long division or some other method to get this

${x}^{2} - 2 - 2$ can be factored normally as $\left(x + 1\right) \left(x - 2\right)$