How do you factor $x^{3} - 2 x$ $x^3 -2x$ ?

Question

4458 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-06T14:45:57

$x (x + \sqrt{2}) (x - \sqrt{2})$ $x(x+sqrt2)(x-sqrt2)$

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

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

$= x (x^{2} - 2)$ $=x(x^2-2)$

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

$x (x^{2} - 2)$ $x(x^2-2)$

$= x (x + \sqrt{2}) (x - \sqrt{2})$ $color(red)(=x(x+sqrt2)(x-sqrt2))$

How do you factor x^3 -2xx3−2xx^3 -2x?