Factorize each of the following algebraic expression:

To factorise $\mathrm{x}^{2}-22 \mathrm{x}+120$, we will find two numbers $\mathrm{p}$ and $\mathrm{q}$ such that $\mathrm{p}+\mathrm{q}=-22$ and $\mathrm{pq}=120$.

Now,

$(-12)+(-10)=-22$

and

$(-12) \times(-10)=120$

Splitting the middle term $-22 \mathrm{x}$ in the given quadratic as $-12 \mathrm{x}-10 \mathrm{x}$, we get:

$\mathrm{x}^{2}-22 \mathrm{x}+12=\mathrm{x}^{2}-12 \mathrm{x}-10 \mathrm{x}+120$

$=\left(\mathrm{x}^{2}-12 \mathrm{x}\right)+(-10 \mathrm{x}+120)$

$=\mathrm{x}(\mathrm{x}-12)-10(\mathrm{x}-12)$

$=(\mathrm{x}-10)(\mathrm{x}-12)$