Factorize:

We have:

$2 x^{2}+11 x-21$

We have to split 11 into two numbers such that their sum is 11 and their product is $(-42)$, i.e., $2 \times(-21)$.

Clearly, $14+(-3)=11$ and $14 \times(-3)=-42$.

$\therefore 2 x^{2}+11 x-21=2 x^{2}+14 x-3 x-21$

$=2 x(x+7)-3(x+7)$

$=(x+7)(2 x-3)$