For which n listed below does there exist a field extension F ɔ Z/2 of degree n such that the polynomialx4 + X² + 1 € F[X] has a root?O n = 1O n = 2O n = 3O n = 4

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Answered: For which na listed below does there…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 5E: Let F be a field and f(x)=a0+a1x+...+anxnF[x]. Prove that x1 is a factor of f(x) if and only if...

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For which na listed below does there exist a field extension F Z/2 of degree n such that the polynomial X4 + X? +1 € F[X] has a root? O n = 1 O n = 2 O n= 3 O n = 4