Question

How do you factor `(x^2-5)`?

Answer 1

`x^2-5 = (x-sqrt(5))(x+sqrt(5))`

Explanation:

The difference of squares identity can be written:

`a^2-b^2=(a-b)(a+b)`

In order to treat `x^2-5` as a difference of squares, we need to recognise that `5 = (sqrt(5))^2`, then we find:

`x^2-5 = x^2-(sqrt(5)^2) = (x-sqrt(5))(x+sqrt(5))`

In other words, we let `a=x` and `b=sqrt(5)`