Question

Factorize:
x² − x − 156

Answer 1

We have:
$x^2-x-156$
We have to split ($-$1) into two numbers such that their sum is ($-$1) and their product is ($-$156).
Clearly, $-13+12=-1\mathrm{and}-13\times 12=-156$.

$$\begin{gathered} \therefore x^2-x-156=x^2-13x+12x-156 \\ =x(x-13)+12(x-13) \\ =(x-13)(x+12) \end{gathered}$$