Question

Factorize:
15x² − x − 128

Answer 1

We have:
$15x^2-x-28$
We have to split ($-$1) into two numbers such that their sum is ($-$1) and their product is ($-$420), i.e., $15\times \left(-28\right)$.
Clearly, $\left(-21\right)+20=-1\mathrm{and}\left(-21\right)\times 20=-420$.

$$\begin{gathered} \therefore 15x^2-x-28=15x^2-21x+20x-28 \\ =3x(5x-7)+4(5x-7) \\ =(5x-7)(3x+4) \end{gathered}$$