The HCF and the LCM of two algebraic expression are (a -5) and $2 a^{3} + 3 a^{2} - 44 a - 105$ respectively. If one of the expressions is $2 a^{2} - 3 a - 35$ , the other will be

a^{2} - 2 a - 15

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a^{2} - 3 a - 10

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a^{2} - 4 a + 15

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2 a^{2} - 5 a + 10

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Solution

The correct option is B $a^{2} - 2 a - 15$
Since, $H . C . F \times L . C . M = one expression \times second expression$
$∴$ Required expression $= \frac{H . C . F . \times L . C . M}{Known expression}$
$= \frac{(a - 5) (2 a^{3} + 3 a^{2} - 44 a - 105)}{2 a^{2} - 3 a - 35}$
$= \frac{(a - 5) (a + 3) (2 a^{2} - 3 a - 35)}{2 a^{2} - 3 a - 35}$
$= (a - 5) (a + 3)$
$= a^{2} - 2 a - 15$ .
Option A is correct.

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