The HCF of (x 3 - y 2 - 2x) and (x 3 + x 2) is

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Let f(x) = x3 - y2 - 2x = x( x2 - x- 2) = x( x2 - 2x + x - 2) = x {x (x - 2) + 1 (x -2)} = x (x +1) (x - 2) and g(x) = x3 + x2 = x2 (x +1) = x. x (x +1) ∴ LCM of [ f(x), g(x)] = x (x +1) . x . (x - 2) = x2(x + 1)(x - 2) = x2(x2 - x - 2) = x4 - x3 - 2x2

The HCF of (x 3 - y 2 - 2x) and (x 3 + x 2) is

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