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Question
Find the LCM pair of the following polynomials
x4 – 27a3x, (x – 3a)2 whose GCD is (x – 3a)
Solution
p(x) = x4 – 27a3x = x[x3 – 27a3]
= x[x3 – (3a)3]
= x(x – 3a) (x2 + 3ax + 9a2)
g(x) = (x – 3a)2
G.C.D. = x – 3a
L.C.M. = `("p"(x) xx "g"(x))/("G"."C"."D".)`
= `(x(x - 3"a")(x^2 + 3"a"x + 9"a"^2) xx (x - 3"a")^2)/((x - 3"a"))`
L.C.M. = x (x – 3a)2 (x2 + 3ax + 9a2)
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