Factorize:

We have:

$x^{2}+18 x+32$

We have to split 18 into two numbers such that their sum is 18 and their product is 32.

Clearly, $16+2=18$ and $16 \times 2=32$

$\therefore x^{2}+18 x+32=x^{2}+16 x+2 x+32$

$=x(x+16)+2(x+16)$

$=(x+16)(x+2)$