Question

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

Answer 1

`2(x-5)(x+4)`

Explanation:

First pull out the factor of 2:
`2x^2-2x-40=2(x^2-x-20)`

For the roots we now need numbers `a,b` that satisfy `ab=-20` and `a+b=-1`. This gives `a=4, b=-5`:
`2(x^2-x-20)=2(x-5)(x+4)`