What is the LCM of x2 2x ndash 8 x3 ndash 4x2 4x and x2 4x ........

Quantitative Aptitude (CGL) Algebra

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What is the LCM of x² + 2x – 8, x³ – 4x² + 4x and x² + 4x?

x(x + 4)(x – 2)²

x(x + 4)(x – 2)

x(x + 4)(x + 2)²

x(x + 4)²(x – 2)

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Explanation:

f(x) = x² + 2x – 8 = x² + 4x – 2x – 8
= x(x + 4) – 2(x + 4) = (x – 2)(x + 4)
g(x) = x³ – 4x² + 4x = x³ – 2x² – 2x² + 4x
= x²(x – 2) – 2x(x – 2) = (x² – 2x)(x – 2)
= x (x – 2) (x – 2)
h(x) = x² + 4x = x(x + 4)
So, LCM of [f(x), g(x), h(x)]
= x(x – 2)(x + 4)(x – 2)
= x(x + 4)(x – 2)²