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

$z^{2}-4 z-12$

$=z^{2}-4 z+\left(\frac{4}{2}\right)^{2}-\left(\frac{4}{2}\right)^{2}-12 \quad\left[\right.$ Adding and subtracting $\left(\frac{4}{2}\right)^{2}$, that is, $\left.2^{2}\right]$

$=z^{2}-4 z+2^{2}-2^{2}-12$

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

$=(z-2)^{2}-4^{2}$

$=[(z-2)-4][(z-2)+4]$

$=(z-6)(z+2)$