Question

Factorize:
x² − 11x − 80

Answer 1

We have:
$x^2-11x-80$
We have to split ($-$11) into two numbers such that their sum is ($-$11) and their product is ($-$80).
Clearly, $-16+5=-11\mathrm{and}-16\times 5=-80$.

$$\begin{gathered} \therefore x^2-11x-80=x^2-16x+5x-80 \\ =x(x-16)+5(x-16) \\ =(x-16)(x+5) \end{gathered}$$