Factorize:

We have:

$2 x^{2}-7 x-15$

We have to split $(-7)$ into two numbers such that their sum is $(-7)$ and their product is $(-30)$, i.e., $2 \times(-15)$.

Clearly, $(-10)+3=-7$ and $(-10) \times 3=-30$

$\therefore 2 x^{2}-7 x-15=2 x^{2}-10 x+3 x-15$

$=2 x(x-5)+3(x-5)$

$=(x-5)(2 x+3)$