Factorize each of the following algebraic expression:

To factorise $\mathrm{x}^{2}+14 \mathrm{x}+45$, we will find two numbers $\mathrm{p}$ and $\mathrm{q}$ such that $\mathrm{p}+\mathrm{q}=14$ and $\mathrm{pq}=45$.

Now,

$9+5=14$

and

$9 \times 5=45$

Splitting the middle term $14 \mathrm{x}$ in the given quadratic as $9 \mathrm{x}+5 \mathrm{x}$, we get:

$\mathrm{x}^{2}+14 \mathrm{x}+45=\mathrm{x}^{2}+9 \mathrm{x}+5 \mathrm{x}+45$

$=\left(\mathrm{x}^{2}+9 \mathrm{x}\right)+(5 \mathrm{x}+45)$

$=\mathrm{x}(\mathrm{x}+9)+5(\mathrm{x}+9)$

$=(\mathrm{x}+5)(\mathrm{x}+9)$