Question

Factorize:
9x² + 18x + 8

Answer 1

We have:
$9x^2+18x+8$
We have to split 18 into two numbers such that their sum is 18 and their product is 72, i.e., $9\times 8$.
Clearly, $12+6=18\mathrm{and}12\times 6=72$.

$$\begin{gathered} \therefore 9x^2+18x+8=9x^2+12x+6x+8 \\ =3x\left(3x+4\right)+2\left(3x+4\right) \\ =\left(3x+4\right)\left(3x+2\right) \end{gathered}$$