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

Oct 6, 2015

$x \left(x + \sqrt{2}\right) \left(x - \sqrt{2}\right)$

#### Explanation:

First, check if there is a common factor that you can take out. In this expression, the common factor is $x$.

${x}^{3} - 2 x$

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

You should be able to recognize that ${x}^{2} - 2$ is a special product (difference of two squares). So you can factor it further:

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

$\textcolor{red}{= x \left(x + \sqrt{2}\right) \left(x - \sqrt{2}\right)}$