H.C.F. and L.C.M. of polynomials \( \Large \left(x-2\right) \), \( \Large x^{2}-4 \) are respectively

A) 1, \( \Large x - 2 \)

B) \( \Large x - 2 \), 8

C) \( \Large x - 2 \), \( \Large x + 2 \)

D) \( \Large x - 2 \), \( \Large x^{2}-4 \)

Correct answer:
D) \( \Large x - 2 \), \( \Large x^{2}-4 \)

Description for Correct answer:

\( \Large x^{2}-4x = \left(x+2\right) \left(x-2\right) \)

\( \Large \therefore L.C.M.\ of\ \left(x-2\right)\ and\ \left(x^{2}-4\right) \)

= \( \Large 1 \times \left(x-2\right) \left(x+2\right) = x^{2}-4 \)

and H.F.C. of \( \Large \left(x-2\right)\ and\ \left(x^{2}-4\right) = x-2 \)



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