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

Jul 21, 2015

$2 \left(x - 5\right) \left(x + 4\right)$
$2 {x}^{2} - 2 x - 40 = 2 \left({x}^{2} - x - 20\right)$
For the roots we now need numbers $a , b$ that satisfy $a b = - 20$ and $a + b = - 1$. This gives $a = 4 , b = - 5$:
$2 \left({x}^{2} - x - 20\right) = 2 \left(x - 5\right) \left(x + 4\right)$