Question

Factorize:
5x² + 16x + 3

Answer 1

We have:
$5x^2+16x+3$
We have to split 16 into two numbers such that their sum is 16 and their product is 15, i.e., $5\times 3$.
Clearly, $15+1=16\mathrm{and}15\times 1=15$.

$$\begin{gathered} \therefore 5x^2+16x+3=5x^2+15x+x+3 \\ =5x\left(x+3\right)+1\left(x+3\right) \\ =\left(x+3\right)\left(5x+1\right) \end{gathered}$$