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Question

Find the L.C.M and H.C.F of two polynomials, p(x) and q(x) are 12(x2−4) and (x−1)(x+3) respectively. If q(x)=4(x+2)(x+3), find p(x).

A
3(x2)(x2)
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B
3(x1)2(x2)
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C
3(x1)(x2)
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D
(x1)(x2)
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Solution

The correct option is C 3(x1)(x2)
Given:
p(x)=?
q(x)=4(x+2)(x+3)
L.C.M =12(x24)=12(x+2)(x2)
So, H.C.F = (x1)(x+3)
Using the formula,
p(x)×q(x)= H.C.F × L.C.M
p(x)=12(x+2)(x2)(x1)(x+3)4(x+2)(x+3)
=3(x1)(x2)
Therefore, p(x) is 3(x1)(x2).

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