Question

Factorize:
2x² − x − 21

Answer 1

We have:
$2x^2-x-21$
We have to split ($-$1) into two numbers such that their sum is ($-$1) and their product is ($-$42), i.e., $2\times \left(-21\right)$.
Clearly, $\left(-7\right)+6=-1\mathrm{and}\left(-7\right)\times 6=-42$.

$$\begin{gathered} \therefore 2x^2-x-21=2x^2+6x-7x-21 \\ =2x(x+3)-7(x+3) \\ =(x+3)(2x-7) \end{gathered}$$