Question

find the LCM and GCD for (x^3-1)(x+1),(x^3-1) and verify that f (x)×g(x)=lcm×gcd​

Answer 1

Answer:

p(x) = (x3 – 1) (x + 1) = (x – 1) (x2 + x + 1) (x + 1) g(x) = x3 + 1 = (x + 1) (x2 – x + 1) G.C.D = (x + 1) L.C.M = (x + 1) (x – 1) (x2 + x + 1) (x2 – x + 1) L.C.M × G.C.D = (x + 1) (x – 1) (x2 + x + 1) (x2 – x + 1) × (x + 1) = (x + 1)2 (x – 1) (x2 + x + 1) (x2 – x + 1) ...(1) p(x) × g(x) = (x – 1) (x2 + x + 1) (x + 1) (x + 1) (x2 – x + 1) = (x + 1)2 (x – 1) (x2 + x + 1) (x2 – x + 1) ...(2) From (1) and (2) we get L.C.M. × G.C.D. = p(x) × g(x)

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