# How do you factor 3x^3-300x?

May 18, 2015

First, let's factor out what both elements share: $3 x$

$3 x \left({x}^{2} - 100\right)$

Now, we can factor the quadratic inside the parenthesis by finding its roots and then turning them into factors:

${x}^{2} = 100$
$x = \sqrt{100}$
$x = \pm 10$

$x = 10$ can be rewritten as $x - 10 = 0$
$x = - 10$ can be rewritten as $x + 10 = 0$

So, rewriting our factors, we have

$3 x \left(x - 10\right) \left(x + 10\right)$