Solve the given question in 20 min plz q2 For which fields Flisted below is the polynomial X4 + X3 +1 € F[X] irreducible?Select all that apply:O Field consisting of 2 elements.O Field consisting of 16 elements.O Field consisting of 3 elements.O Fraction field of the polynomial ring R[Y].

Given F is a field and fX=X4+X3+1 ∈FX. We have to select the correct option for which the given…

Answered: For which fields F listed below is the…

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 1E

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For which fields F listed below is the polynomial X + X3 +1 € F[X] irreducible? Select all that apply: O Field consisting of 2 elements. O Field consisting of 16 elements. O Field consisting of 3 elements. O Fraction field of the polynomial ring RY].