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GCD by Factorization

The L.C.M. of...

Question

The L.C.M. of $x^{3} - 8$ and $x^{2} - 5 x + 6$ is

x - 2

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x^{2} + 2 x + 4

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(x - 2) (x^{2} + 2 x + 4)

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(x - 2) (x - 3) (x^{2} + 2 x + 4)

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Solution

The correct option is D $(x - 2) (x - 3) (x^{2} + 2 x + 4)$
$x^{3} - 8 = (x - 2) (x^{2} + 2 x + 4)$
$(x^{2} - 5 x + 6) = (x - 2) (x - 3)$
$∴ L C M = (x - 2) (x - 3) (x^{2} - 2 x + 4)$
LCM is taking highest
Power of terms b/w 2
Polynomials

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p (x)

g (x)

q (x)

r (x)

p (x)

(\frac{x - 3}{x^{2} - x - 6} + \frac{2 x - 1}{2 x^{2} + 5 x - 3} - \frac{2 x + 5}{x^{2} + 5 x + 6})

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