Question

Factorize:
14x² + 9x + 1

Answer 1

We have:
$14x^2+9x+1$

We have to split 9 into two numbers such that their sum is 9 and their product is 14, i.e., $14\times 1$.
Clearly, $7+2=9\mathrm{and}7\times 2=14$.

$$\begin{gathered} \therefore 14x^2+9x+1=14x^2+2x+7x+1 \\ =2x\left(7x+1\right)+1\left(7x+1\right) \\ =\left(7x+1\right)\left(2x+1\right) \end{gathered}$$