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

$p^{2}-10 q+21$

$=\mathrm{q}^{2}-10 \mathrm{q}+\left(\frac{10}{2}\right)^{2}-\left(\frac{10}{2}\right)^{2}+21 \quad$ Adding and subtracting $\left(\frac{10}{2}\right)^{2}$, that is, $\left.5^{2}\right]$

$=\mathrm{q}^{2}-2 \times \mathrm{q} \times 5+5^{2}-5^{2}+21$

$=(\mathrm{q}-5)^{2}-4 \quad[$ Completing the square $]$

$=(q-5)^{2}-2^{2}$

$=[(q-5)-2][(q-5)+2]$

$=(q-5-2)(q-5+2)$

$=(q-7)(q-3)$