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Question

Find the GCD of the following polynominals 3x4+6x312x224x and 4x4+x3+8x28x.

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Solution

Let f(x)=3x4+6x312x224x=3x(x3+2x24x8).
Let g(x)=4x4+14x3+8x28x=2x(2x3+7x2+4x4)
LetusfindtheGCDforthepolynomials x3+2x24x8 and 2x3+7x2+4x4
We choose the divisor to bex3+2x24x8.
Common factor of x3+2x24x8 and2x3+7x2+4x4 isx2+4x+4
Also common factor of 3x and 2x is x.Thus,GCD (f(x),g(x))=x(x2+4x+4).
1074948_624696_ans_7a89949919fa4b689a755ef416dbdf78.PNG

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