Determine the greatest common divisor of the polynomials X4 +X² + 1 and X³ + X³ + X² + 1 in F[X], whereFis a field consisting of 8 elements.Select one:O The gcd is X? +1O The gcd is X +1O The gcd is X3 + X + 1O The gcd is X? + X +1cross outcross outcross outcross out

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 13E

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Determine the greatest common divisor of the polynomials X4 + X? +1 and X5 + X3 + x² +1 in F[X], where Fis a field consisting of 8 elements. Select one: O The gcd is X? + 1 O The gcd is X +1 O The gcd is X3 + X +1 O The gcd is X2 + X +1 cross out cross out cross out cross out