The product of two expression is $x^{3} + x^{2} - 44 x - 84$ . If the HCF of these two expressions is $(x + 6)$ , then their LCM will be

(x + 2) (x + 7)

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(x + 2) (x - 7)

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(x - 2) (x + 7)

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(x - 2) (x - 7)

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Solution

The correct option is B $(x + 2) (x - 7)$
LCM x HCF = Product of the expressions
$\Rightarrow L C M = \frac{P r o d . o f e x p r e s s i o n s}{H C F}$
= $\frac{x^{3} + x^{2} - 44 x - 84}{(x + 6)}$
$∴$ Reqd LCM = $x^{2} - 5 x - 14 = (x - 7) (x + 2)$

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