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Factorisation Using Algebraic Identities

Factorise the...

Question

Factorise the following: $6 x^{2} - 5 x - 14$

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Solution

Given: $6 x^{2} - 5 x - 14$
$= 6 x^{2} - 12 x + 7 x - 14$ , (split the middle term)
$= (6 x^{2} - 12 x) + (7 x - 14)$ , (group pair of terms)
$= 6 x (x - 2) + 7 (x - 2)$ ,( factor each binomials)
$= (x - 2) (6 x + 7)$ , (factor out common factor $(x - 2)$ )

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