# How do you factor x^4-6x^2-16?

Jun 7, 2015

${x}^{4} - 6 {x}^{2} - 16$

$= {\left({x}^{2}\right)}^{2} - 6 \left({x}^{2}\right) - 16$

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

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

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

$\left({x}^{2} + 2\right)$ has no simpler factors with real coefficients,

since $\left({x}^{2} + 2\right) \ge 2$ so ${x}^{2} + 2 = 0$ has no roots for all $x \in \mathbb{R}$.