Resolve each of the following quadratic trinomial into factor:

The given expression is $3 \mathrm{x}^{2}+10 \mathrm{x}+3 . \quad$ (Coefficient of $\mathrm{x}^{2}=3$, coefficient of $\mathrm{x}=10$ and constant term $=3$ )

We will split the coefficient of $\mathrm{x}$ into two parts such that their sum is 10 and their product equals the product of the coefficient of $\mathrm{x}^{2}$ and the constant term, i. e., $3 \times 3=9$.

Now,

$9+1=10$

and

$9 \times 1=9$

Replacing the middle term $10 \mathrm{x}$ by $9 \mathrm{x}+\mathrm{x}$, we have:

$3 \mathrm{x}^{2}+10 \mathrm{x}+3=3 \mathrm{x}^{2}+9 \mathrm{x}+\mathrm{x}+3$

$=\left(3 \mathrm{x}^{2}+9 \mathrm{x}\right)+(\mathrm{x}+3)$

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

$=(3 \mathrm{x}+1)(\mathrm{x}+3)$