Factorize each of the following algebraic expression:

To factorise $x^{2}-11 x-42$, we will find two numbers $p$ and $q$ such that $p+q=-11$ and $p q=-42$.

Now,

$3+(-14)=-22$

and

$3 \times(-14)=42$

Splitting the middle term $-11 \mathrm{x}$ in the given quadratic as $-14 \mathrm{x}+3 \mathrm{x}$, we get:

$\mathrm{x}^{2}-11 \mathrm{x}-42=\mathrm{x}^{2}-14 \mathrm{x}+3 \mathrm{x}-42$

$=\left(x^{2}-14 x\right)+(3 x-42)$

$=x(x-14)+3(x-14)$

$=(x+3)(x-14)$