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The LCM of (x3 – x2 – 2x) and (x3 + x2) is
x3 – x2 – 2x
x2 + x
x4 – x3 – 2x2
x – 2
Let f(x) = (x3 – x2 – 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.
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