Question

Factorize:
10x² − 9x − 7

Answer 1

We have:
$10x^2-9x-7$

We have to split ($-$9) into two numbers such that their sum is ($-$9) and their product is ($-$70), i.e., $10\times \left(-7\right)$.
Clearly, $\left(-14\right)+5=-9\mathrm{and}\left(-14\right)\times 5=-70$.

$$\begin{gathered} \therefore 10x^2-9x-7=10x^2+5x-14x-7 \\ =5x\left(2x+1\right)-7\left(2x+1\right) \\ =\left(2x+1\right)\left(5x-7\right) \end{gathered}$$