Question

Factorize:
18x² + 3x − 10

Answer 1

We have:
$18x^2+3x-10$
We have to split 3 into two numbers such that their sum is 3 and their product is ($-$180), i.e., $18\times \left(-10\right)$.
Clearly, $15+\left(-12\right)=3\mathrm{and}15\times \left(-12\right)=-180$.

​$$\begin{gathered} \therefore 18x^2+3x-10=18x^2+15x-12x-10 \\ =3x\left(6x+5\right)-2\left(6x+5\right) \\ =\left(6x+5\right)\left(3x-2\right) \end{gathered}$$