Question

Factorize:
6x² + 11x − 10

Answer 1

We have:
$6x^2+11x-10$
We have to split 11 into two numbers such that their sum is 11 and their product is ($-$60), i.e., $6\times \left(-10\right)$.
Clearly, $15+\left(-4\right)=11\mathrm{and}15\times \left(-4\right)=-60$.

$$\begin{gathered} \therefore 6x^2+11x-10=6x^2+15x-4x-10 \\ =3x\left(2x+5\right)-2\left(2x+5\right) \\ =\left(2x+5\right)\left(3x-2\right) \end{gathered}$$