Question

Factorize:
15x² + 2x − 8

Answer 1

We have:
$15x^2+2x-8$
We have to split 2 into two numbers such that their sum is 2 and their product is ($-$120), i.e., $15\times \left(-8\right)$.
Clearly, $12+\left(-10\right)=2\mathrm{and}12\times \left(-10\right)=-120$.

$$\begin{gathered} \therefore 15x^2+2x-8=15x^2+12x-10x-8 \\ =3x\left(5x+4\right)-2\left(5x+4\right) \\ =\left(5x+4\right)\left(3x-2\right) \end{gathered}$$