Factorise:
$2 x^{3} - 3 x^{2} - 17 x + 30$

(x - 2) (x + 4) (2 x - 5)

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(x - 2) (x + 2) (2 x - 5)

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(x - 2) (x + 1) (2 x - 5)

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(x - 2) (x + 3) (2 x - 5)

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Solution

The correct option is D $(x - 2) (x + 3) (2 x - 5)$
$2 x^{3} - 3 x^{2} - 17 x + 30$
$= 2 x^{3} + 2 x^{2} - 12 x - 5 x^{2} - 5 x + 30$
$= 2 x (x^{2} + x - 6) - 5 (x^{2} + x - 6)$
$= (x^{2} + x - 6) (2 x - 5)$
$= (x^{2} + 3 x - 2 x - 6) (2 x - 5)$
$= [x (x + 3) - 2 (x + 3)] (2 x - 5)$
$= (x + 3) (x - 2) (2 x - 5)$

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