Factorize each of the following algebraic expression:

To factorise $\mathrm{a}^{2}-14 \mathrm{a}-51$, we will find two numbers $\mathrm{p}$ and $\mathrm{q}$ such that $\mathrm{p}+\mathrm{q}=-14$ and $\mathrm{pq}=-51$.

Now,

$3+(-17)=-14$

and

$3 \times(-17)=-51$

Splitting the middle term $-14 \mathrm{a}$ in the given quadratic as $3 \mathrm{a}-17 \mathrm{a}$, we get:

$a^{2}-14 a-51=a^{2}+3 a-17 a-51$

$=\left(a^{2}+3 a\right)-(17 a+51)$

$=a(a+3)-17(a+3)$

$=(a-17)(a+3)$