Resolve each of the following quadratic trinomial into factor:

The given expression is $2 \mathrm{x}^{2}+5 \mathrm{x}+3$.            (Coefficient of $x^{2}=2$, coefficient of $x=5$ and constant term =3)

We will split the coefficient of $\mathrm{x}$ into two parts such that their sum is 5 and their product equals th product of the coefficient of $\mathrm{x}^{2}$ and the constant term, i.e., $2 \times 3=6$.

Now,

$2+3=5$

and

$2 \times 3=6$

Replacing the middle term $5 \mathrm{x}$ by $2 \mathrm{x}+3 \mathrm{x}$, we have :

$2 \mathrm{x}^{2}+5 \mathrm{x}+3=2 \mathrm{x}^{2}+2 \mathrm{x}+3 \mathrm{x}+3$

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

$=2 \mathrm{x}(\mathrm{x}+1)+3(\mathrm{x}+1)$

$=(\mathrm{x}+1)(2 \mathrm{x}+3)$