Question

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

Answer 1

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

Explanation:

Note that:

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

So if we can find two positive numbers `a, b` such that `a-b=1` and `ab = 12` then we have a factorisation.

The numbers `a=4` and `b=3` work, so we find:

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