Resolve each of the following quadratic trinomial into factor:

The given expression is $3 \mathrm{x}^{2}+22 \mathrm{x}+35$.         (Coefficient of $\mathrm{x}^{2}=3$, coefficient of $\mathrm{x}=22$ and constant term $=35$ )

We will split the coefficient of $\mathrm{x}$ into two parts such that their sum is 22 and their product equals the product of the coefficient of $\mathrm{x}^{2}$ and the constant term, i.e., $3 \times 35=105$.

Now,

$15+7=22$

and

$15 \times 7=105$

Replacing the middle term $22 \mathrm{x}$ by $15 \mathrm{x}+7 \mathrm{x}$, we get:

$3 x^{2}+22 x+35=3 x^{2}+15 x+7 x+35$

$=\left(3 \mathrm{x}^{2}+15 \mathrm{x}\right)+(7 \mathrm{x}+35)$

$=3 \mathrm{x}(\mathrm{x}+5)+7(\mathrm{x}+5)$

$=(3 \mathrm{x}+7)(\mathrm{x}+5)$