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Factorisation Using Algebraic Identities

Factorise : ...

Question

Factorise : $6 x^{2} - 5 x - 21$

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Solution

Given : $6 x^{2} - 5 x - 21$
Splitting the middle term as follows:
$6 x^{2} - 5 x - 21$ $= 6 x^{2} + 9 x - 14 x - 21$
Taking out the common terms:
$6 x^{2} - 5 x - 21$ $= 3 x (2 x + 3) - 7 (2 x + 3)$
So we get,
$6 x^{2} - 5 x - 21$ $= (3 x - 7) (2 x + 3)$

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