Question

L.C.M. of \(x^3 - 9x\) and \(x^2 - 2x - 3\) is

• A. \(x - 3\)
• B. \(x + 3\)
• C. \(x(x + 1)\)
• D. \(x(x + 3)(x - 3)\)

Hint:

To find the L.C.M. of polynomials, factorize them and take all distinct factors.

Answer 1

The Correct Option is D

We begin by factoring both expressions: \[ x^3 - 9x = x(x^2 - 9) = x(x - 3)(x + 3) \] \[ x^2 - 2x - 3 = (x - 3)(x + 1) \] The L.C.M. is the product of all distinct factors: \[ \text{L.C.M.} = x(x - 3)(x + 3)(x + 1) \] Thus, the correct answer is \(x(x + 3)(x - 3)\).