Evaluate the H.C.F and L.C.M of the polynomial $(x + 4)^{3} (x + 1)$ and $(x + 1) (x^{2} + 4 x + 16)$ .

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Solution

Let $f (x) =$ $(x + 4)^{3} (x + 1)$ and $g (x) =$ $(x + 1) (x^{2} + 4 x + 16)$ .
Factor of $x^{2} + 4 x + 16 = (x + 4)^{2}$
So, H.C.F $=$ $(x + 4)^{2} (x + 1)$
L.C.M $=$ $(x + 4)^{3} (x + 1)$

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