Question

How do you factor the trinomial `x^2-x-12`?

Answer 1

`x^2-x-12 = (x-4)(x+3)`

Explanation:

Look for a pair of factors of `12` that differ by `1`. The pair `4, 3` works.

Hence we find:

`x^2-x-12 = (x-4)(x+3)`

In general:

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

In our case we found `a=4`, `b=3` giving `a-b=1` and `ab=12`