Question

How do you factor: `y=x^2 - 5`?

Answer 1

Apply the difference of squares formula to find that
`x^2 - 5 = (x + sqrt(5))(x - sqrt(5))`

Explanation:

The difference of squares formula states that
`a^2 - b^2 = (a+b)(a-b)`
(This is easy to verify by expanding the right hand side)

While `5` may not be a perfect square, it is still the square of something... specifically, it is the square of `sqrt(5)`
Then, applying the formula, we have

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