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Question
Find the G.C.D. of the given polynomials
3x3 + 3x2 + 3x + 3, 6x3 + 12x2 + 6x + 12
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Solution
p(x) = 3x3 + 3x2 + 3x + 3
= 3(x3 + x2 + x + 1)
g(x) = 6x3 + 12x2 + 6x + 12
= 6(x3 + 2x2 + x + 2)
G.C.D. of 3 and 6 = 3
Now g(x) is divided by p(x)
Now dividing p(x) by the remainder x2 + 1
we get x + 1
∴ G.C.D. = 3(x2 + 1) ...[3 is the G.C.D. of 3 and 6]
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