Question

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

Answer 1

Please see below.

Explanation:

If we are to use integers only, we factor it as

`5x^2-40 = 5(x^2-8)`

Since `sqrt8 = 2sqrt2` 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

`5x^2-40 = 5(x^2-8) = 5(x+sqrt8)(x-sqrt8) = 5(x+2sqrt2)(x-2sqrt2)`