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Question
Find the GCD of the following by division algorithm
2x4 + 13x3 + 27x2 + 23x + 7, x3 + 3x2 + 3x + 1, x2 + 2x + 1
Solution
p(x) = 2x4 + 13x3 + 27x2 + 23x + 7
g(x) = x3 + 3x2 + 3x + 1
r(x) = x2 + 2x + 1
(i) Find the G.C.D. of p(x) and g(x)
∴ G.C.D. = x3 + 3x2 + 3x + 1
(ii) Find the G.C.D. of r(x) and the G.C.D. of p(x) and g(x)
∴ G.C.D. = x2 + 2x + 1
∴ G.C.D. of the three polynomials = x2 + 2x + 1
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