Factorize:

We have:

$x^{2}+11 x+30$

We have to split 11 into two numbers such that their sum of is 11 and their product is 30.

Clearly, $5+6=11$ and $5 \times 6=30$

$\therefore x^{2}+11 x+30=x^{2}+5 x+6 x+30$

$=x(x+5)+6(x+5)$

$=(x+5)(x+6)$