Factorise the following: $3 x^{2} - 17 x + 20$

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Solution

Given: $3 x^{2} - 17 x + 20$
$= 3 x^{2} - 12 x - 5 x + 20$ , (split middle term)
$= (3 x^{2} - 12 x) + (- 5 x + 20)$ , (group pair of terms)
$= 3 x (x - 4) - 5 (x - 4)$ , (factor each binomials)
$= (x - 4) (3 x - 5)$ , (factor out common factor $(x - 4)$ )

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