$10 (u^{3} + 64), 15 (u^{2} - 16)$ are the two polynomials. What is their H.C.F and L.C.M?

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Solution

Let $f (x) =$ $10 (u^{3} + 64)$ , g(x) = $15 (u^{2} - 16)$
Factor of $(u^{3} + 4^{3}) = (u + 4) (u^{2} + 4 u + 16)$
Factor of $(u^{2} - 4^{2}) = (u + 4) (u - 4)$
Factor of $10 = 2 \times 5$
Factor of $15 = 3 \times 5$
So, H.C.F $= 5$
Therefore, H.C.F of the polynomial is $5 (u + 4)$
L.C.M of the polynomial $=$ $30 (u + 4) (u - 4) (u^{2} + 4 u + 16)$

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