Calculate H.C.F and L.C.M of the polynomial $12 (x^{3} - 1)$ and $3 (x - 1)$ .

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Solution

Let $f (x) =$ $12 (x^{3} - 1)$ and g(x) = $3 (x - 1)$
We know that $x^{3} - 1 = (x - 1) (x^{2} + x + 1)$
Factors of $12$ are: $1, 2, 3, 4, 6, 12$
Factors of $3$ are: $1, 3$
So, H.C.F of $12$ and $3$ is $3$
Therefore, H.C.F $=$ $3 (x - 1)$
L.C.M of $12$ and $3$ is $12$
So, L.C.M $=$ $12 (x - 1) (x^{2} + x + 1)$

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