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Question
Find the GCD pair of the following polynomials
12(x4 – x3), 8(x4 – 3x3 + 2x2) whose LCM is 24x3 (x – 1)(x – 2)
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Solution
p(x) = 12(x4 – x3)
= 12x3(x – 1)
g(x) = 8(x4 – 3x3 + 2x2)
= 8x2(x2 – 3x + 2)
= 8x2(x – 2)(x – 1)
L.C.M. = 24x3 (x – 1) (x – 2)
G.C.D. = `("p"(x) xx "g"(x))/("L"."C"."M".)`
= `(12x^3 (x - 1) xx 8x^2 (x - 2)(x - 1))/(24x^3 (x - 1) (x - 2))`
G.C.D. = 4x2(x – 1)
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