Question

Factorize:
5x² − 16x − 21

Answer 1

We have:
$5x^2-16x-21$
We have to split ($-$16) into two numbers such that their sum is ($-$16) and their product is ($-$105), i.e., $5\times \left(-21\right)$.
Clearly, $\left(-21\right)+5=-16\mathrm{and}\left(-21\right)\times 5=-105$.

$$\begin{gathered} \therefore 5x^2-16x-21=5x^2+5x-21x-21 \\ =5x\left(x+1\right)-21\left(x+1\right) \\ =\left(x+1\right)\left(5x-21\right) \end{gathered}$$