Question

Factorize:
2x² + 11x − 21

Answer 1

We have:
$2x^2+11x-21$
We have to split 11 into two numbers such that their sum is 11 and their product is ($-$42), i.e., $2\times \left(-21\right)$.
Clearly, $14+\left(-3\right)=11\mathrm{and}14\times \left(-3\right)=-42$.

$$\begin{gathered} \therefore 2x^2+11x-21=2x^2+14x-3x-21 \\ =2x\left(x+7\right)-3\left(x+7\right) \\ =\left(x+7\right)\left(2x-3\right) \end{gathered}$$