# How do you factor 32x^5 + 64x^4 + 16x?

Mar 30, 2018

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

#### Explanation:

1) Factor
You can factor 16 out of all three terms
$16 \left(2 {x}^{5} + 4 {x}^{4} + x\right)$
You can also factor $x$ from all three terms
$16 x \left(2 {x}^{4} + 4 {x}^{3} + 1\right)$

2) You plug it into the quadratic formula.
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
You get the roots of
$x = - \frac{2 + \sqrt{2}}{2} , \frac{\sqrt{2} - 2}{2}$

3) You make them factored
$\left(x + \frac{2 + \sqrt{2}}{2}\right) \left(x - \frac{\sqrt{2} - 2}{2}\right)$