Question:
Factorize:
$15 x^{2}-x-128$
Solution:
We have:
$15 x^{2}-x-28$
We have to split $(-1)$ into two numbers such that their sum is $(-1)$ and their product is $(-420)$, i.e., $15 \times(-28)$.
Clearly, $(-21)+20=-1$ and $(-21) \times 20=-420$.
$\therefore 15 x^{2}-x-28=15 x^{2}-21 x+20 x-28$
$=3 x(5 x-7)+4(5 x-7)$
$=(5 x-7)(3 x+4)$
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