The L.C.M. of $6 x^{2} - x - 1, 3 x^{2} + 7 x + 2$ and $2 x^{2} + 3 x - 2$ is .

(x + 2) (2 x - 1) (3 x + 1)

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(2 x - 1) (3 x + 1)

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(2 x + 1) (3 x - 1)

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(x + 2) (2 x + 1) (3 x - 1)

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Solution

The correct option is A $(x + 2) (2 x - 1) (3 x + 1)$
First expression:
$6 x^{2} - x - 1 = 6 x^{2} - 3 x + 2 x - 1 = 3 x (2 x - 1) + 1 (2 x - 1) = (3 x + 1) (2 x - 1)$

Second expression:
$3 x^{2} + 7 x + 2 = 3 x^{2} + 6 x + x + 2 = 3 x (x + 2) + 1 (x + 2) = (3 x + 1) (x + 2)$

Third expression:
$2 x^{2} + 3 x - 2 = 2 x^{2} + 4 x - x - 2 = 2 x (x + 2) - 1 (x + 2) = (2 x - 1) (x + 2)$

Hence the required L.C.M. is $(x + 2) (2 x - 1) (3 x + 1) .$

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