Find the L.C.M. m(x) of p (x) $= 4^{3} + 108$ and q(x) $= 6 x^{2} + 42 x + 72.$

8 (x - 3) (x^{2} + 3 x + 9) (x + 4)

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12 (x - 3) (x^{2} - 3 x - 9) (x - 4)

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12 (x - 3) (x^{2} + 3 x x + 9) (x - 4)

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12 (x + 3) (x^{2} - 3 x + 9) (x + 4)

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Solution

The correct option is D $12 (x + 3) (x^{2} - 3 x + 9) (x + 4)$
$p (x) = 4 x x^{3} + 108 = 4 (x^{3} + 27)$
$= 4 (x + 3) (x^{2} - 3 x + 9) = 2^{2} (x + 3) (x^{2} - 3 x + 9)$
$q (x) = 6 x^{2} + 42 x + 72 = 6 (x^{2} + 7 x + 12)$
$= 6 (x + 3) (x + 4) = 2 \times 3 (x + 3) (x + 4)$
Thus, the L.C.M. m(x) of p(x) and q(x)
$= 2^{2} \times 3 (x + 3) + (x^{2} - 3 x + 9) \times (x + 4)$
$= 12 (x + 3) (x^{2} - 3 x + 9) (x + 4)$

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