H.C.F of two polynomials is a + 5 and L.C.M is (a +5) (a + 4 )(a -1).1f one of the polynomials is $a^{2} + 4 a - 5$ , then the other polynomial is

a^{2} + 9 a - 20

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a^{2} - 9 a + 20

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a^{2} + 9 a + 20

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a^{2} - 9 a - 20

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Solution

The correct option is C $a^{2} + 9 a + 20$
Since, LCM $\times$ HCF = 1st polynomial $\times$ 2nd polynomial
$∴$ Other polynomial $= \frac{L C M \times H C F}{1st Polynomial}$
$= \frac{(a + 5) (a + 4) (a - 1) (a + 5)}{a^{2} + 4 a - 5}$
$= \frac{(a + 5) (a + 4) (a - 1) (a + 5)}{(a + 5) (a - 1)}$
$= (a + 4) (a + 5)$
$= a^{2} + 9 a + 20$
Option C is correct.

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