# How do you factor completely 5x^2 − 40?

Oct 1, 2017

$5 {x}^{2} - 40 = 5 \left({x}^{2} - 8\right)$
Since $\sqrt{8} = 2 \sqrt{2}$ is irrational, we do not continue unless we are fartoring using all real numbers. If we are allowed to use any real number, we factor it as
$5 {x}^{2} - 40 = 5 \left({x}^{2} - 8\right) = 5 \left(x + \sqrt{8}\right) \left(x - \sqrt{8}\right) = 5 \left(x + 2 \sqrt{2}\right) \left(x - 2 \sqrt{2}\right)$