The L.C.M. of $9 x^{2} + 6 x + 1, 3 x^{2} + 7 x + 2 a n d 2 x^{2} + 3 x - 2$ is $(x + a) (2 x - b) (3 x + c)^{2}$ . Then the value of $a - b - c = ?$

$3$

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$6$

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$0$

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$9$

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Solution

The correct option is C
$0$

First expression = $9 x^{2} + 6 x + 1 = (3 x + 1)^{2}$
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= $2 x^{2} + 3 x - 2 = 2 x^{2} + 4 x - x - 2 = 2 x (x + 2) - 1 (x + 2) = (2 x - 1) (x + 2)$
Required L.C.M. is $(x + 2) (2 x - 1) (3 x + 1)^{2}$

$a = 2, b = 1, c = 1$

$a - b - c = 0$

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Similar questions

If the L.C.M. of $9 x^{2} + 6 x + 1, 3 x^{2} + 7 x + 2 a n d 2 x^{2} + 3 x - 2$ is $(x + a) (2 x - b) (3 x + c)^{2}$ . Find value of $a - b - c =$

9 x^{2} + 6 x + 1, 3 x^{2} + 7 x + 2

2 x^{2} + 3 x - 2

(x + a) (2 x - b) (3 x + c)^{2}

a - b - c =

6 x^{2} - x - 1, 3 x^{2} + 7 x + 2

2 x^{2} + 3 x - 2

L.C.M. of $6 x^{2} - x - 1, 3 x^{2} + 7 x + 2 a n d 2 x^{2} + 3 x - 2$ is $(x + 2) (2 x - 1) (3 x + 1)$

Find the L.C.M. of $6 x^{2} - x - 1, 3 x^{2} + 7 x + 2 a n d 2 x^{2} + 3 x - 2$

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