Question

Factorize:
30x² + 7x − 15

Answer 1

We have:
$30x^2+7x-15$

We have to split 7 into two numbers such that their sum is 7 and their product is ($-$450), i.e., $30\times \left(-15\right)$.
Clearly, $25+\left(-18\right)=7\mathrm{and}25\times \left(-18\right)=-450$.

$$\begin{gathered} \therefore 30x^2+7x-15=30x^2+25x-18x-15 \\ =5x\left(6x+5\right)-3\left(6x+5\right) \\ =\left(6x+5\right)\left(5x-3\right) \end{gathered}$$