Question

Factorize:
6x² − 5x − 21

Answer 1

We have:
$6x^2-5x-21$
We have to split ($-$5) into two numbers such that their sum is ($-$5) and their product is ($-$126), i.e., $6\times \left(-21\right)$.
Clearly, $9+\left(-14\right)=-5\mathrm{and}9\times \left(-14\right)=-126$.

$$\begin{gathered} \therefore 6x^2-5x-21=6x^2+9x-14x-21 \\ =3x\left(2x+3\right)-7\left(2x+3\right) \\ =\left(2x+3\right)\left(3x-7\right) \end{gathered}$$