Question

Factorize:
2x² + 3x − 90

Answer 1

We have:
$2x^2+3x-90$
We have to split 3 into two numbers such that their sum is 3 and their product is ($-$180), i.e., $2\times \left(-90\right)$.
Clearly, $-12+15=3\mathrm{and}-12\times 15=-180$.

$$\begin{gathered} \therefore 2x^2+3x-90=2x^2-12x+15x-90 \\ =2x\left(x-6\right)+15\left(x-6\right) \\ =\left(x-6\right)\left(2x+15\right) \end{gathered}$$