Factorise 10 x^{2}-x-24 by splitting middle term.

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2. Polynomials

easy

Factorise $10 x^{2}-x-24$ by splitting the middle term.

Option A

Option B

Option C

Option D

Solution

If we can find two numbers $p$ and $q$ such that $p+q=-1$ and

$p q=(10)(-24)=-240,$ then we can get the factors.

$p=15$ and $q=-16$ satisfy $p+q=1$ and $p q=-240$

So, $10 x^{2}-x-24$

$=10 x^{2}+15 x-16 x-24$

$=5 x(2 x+3)-8(2 x+3)$

$=(2 x+3)(5 x-8)$

$10 \times(-24)=-240$

$(-240)=15 \times(-16)$

$15+(-16)=-1$

Standard 9

Mathematics

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