How do you factor completely 2x^2 + 2x -40?

May 24, 2016

$2 {x}^{2} + 2 x - 40 = 2 \left(x - 4\right) \left(x + 5\right)$

Explanation:

To factorize a quadratic polynomial of type $a {x}^{2} + b x + c$,

one needs to split middle term $b$ in two parts whose product is $a c$. As in $2 {x}^{2} + 2 x - 40$, the product is $- 80$, these are $10$ and $- 8$.

Hence, $2 {x}^{2} + 2 x - 40$

= $2 {x}^{2} + 10 x - 8 x - 40$

= $2 x \left(x + 5\right) - 8 \left(x + 5\right)$

= $\left(2 x - 8\right) \left(x + 5\right)$

= $2 \left(x - 4\right) \left(x + 5\right)$