Factorize each of the following quadratic polynomials by using the method of completing the square:

$x^{2}+12 x+20$

$=x^{2}+12 x+\left(\frac{12}{2}\right)^{2}-\left(\frac{12}{2}\right)^{2}+20 \quad\left[\right.$ Adding and subtracting $\left(\frac{12}{2}\right)^{2}$, that is, $\left.6^{2}\right]$

$=x^{2}+12 x+6^{2}-6^{2}+20$

$=(x+6)^{2}-16 \quad[$ Completing the square $]$

$=(x+6)^{2}-4^{2}$

$=[(x+6)-4][(x+6)+4]$

$=(x+6-4)(x+6+4)$

$=(x+2)(x+10)$