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

$p^{2}+6 p+8$

$=\mathrm{p}^{2}+6 \mathrm{p}+\left(\frac{6}{2}\right)^{2}-\left(\frac{6}{2}\right)^{2}+8 \quad$ [Adding and subtracting $\left(\frac{6}{2}\right)^{2}$, that is, $\left.3^{2}\right]$

$=\mathrm{p}^{2}+6 \mathrm{p}+3^{2}-3^{2}+8$

$=\mathrm{p}^{2}+2 \times \mathrm{p} \times 3+3^{2}-9+8$

$=\mathrm{p}^{2}+2 \times \mathrm{p} \times 3+3^{2}-1$

$=(\mathrm{p}+3)^{2}-1^{2} \quad[$ Completing the square $]$

$=[(\mathrm{p}+3)-1][(\mathrm{p}+3)+1]$

$=(\mathrm{p}+3-1)(\mathrm{p}+3+1)$

$=(\mathrm{p}+2)(\mathrm{p}+4)$