Question

Factorize:
6x² + 17x + 12

Answer 1

We have:
$6x^2+17x+12$
We have to split 17 into two numbers such that their sum is 17 and their product is 72, i.e., $6\times 12$.
Clearly, $8+9=17\mathrm{and}8\times 9=72$.

$$\begin{gathered} \therefore 6x^2+17x+12=6x^2+8x+9x+12 \\ =2x\left(3x+4\right)+3\left(3x+4\right) \\ =\left(3x+4\right)\left(2x+3\right) \end{gathered}$$