Find the L.C.M of $x^{3} - 2 x^{2} - 13 x - 10 = 0$ and $x^{3} - x^{2} - 10 x - 8$

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Solution

By factorizing the polynomials, we get
$x^{3} - 2 x^{2} - 13 x - 10 = (x + 1) (x^{2} - 3 x - 10) = (x + 1) (x + 2) (x - 5)$
$x^{3} - x^{2} - 10 x - 8 = (x + 1) (x^{2} - 2 x - 8) = (x + 1) (x + 2) (x - 4)$

From the above factors, we can see that, H.C.F. $= (x + 1) (x + 2)$
And L.C.M. $= (x + 1) (x + 2) (x - 4) (x - 5)$

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