What is the g. c. d of f(x) = x^4+x^3+1 and g(x) x^2+x+1 in z11[x]​

Question

What is the g. c. d of f(x) = x^4+x^3+1 and g(x) x^2+x+1 in z11[x]​

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Lyla 1 month 2021-08-12T19:36:03+00:00 1 Answer 0 views 0

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    2021-08-12T19:37:57+00:00

    Answer:

    factors of f(x) are

     \sqrt{ \ \frac{ - 1 +  i\sqrt{3} }{2}  }  \: and \:  \sqrt{ \frac{ - 1 - i \sqrt{3}  }{2} }

    factors of g(x) are

     \frac{ - 1 + i  \sqrt{3} }{2}  \: and \:  \frac{ - 1 - i \sqrt{3} }{2}

    now factors for GCD will be same in f(x)

    I hope the above solution helps

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