# How do you factor x^4 + 8x^3 - 2x^2 - 16x?

Apr 9, 2016

${x}^{4} + 8 {x}^{3} - 2 {x}^{2} - 16 x = x \left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right) \left(x + 8\right)$

#### Explanation:

First note that all of the terms are divisible by $x$, so separate that out as a factor first, then factor by grouping...

${x}^{4} + 8 {x}^{3} - 2 {x}^{2} - 16 x$

$= x \left({x}^{3} + 8 {x}^{2} - 2 x - 16\right)$

$= x \left(\left({x}^{3} + 8 {x}^{2}\right) - \left(2 x + 16\right)\right)$

$= x \left({x}^{2} \left(x + 8\right) - 2 \left(x + 8\right)\right)$

$= x \left({x}^{2} - 2\right) \left(x + 8\right)$

$= x \left(x - \sqrt{2}\right) \left(x + \sqrt{2}\right) \left(x + 8\right)$