Answered: Show that the following polynomials are…

Show that the following polynomials are irreducible over Z[r]. fi(x) = 17r³ + 7x + 3, f2(r) = 2r* + 3r² +x – 2, fa(x) = 7xª + 5x – 3.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 17E

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Question

Show that the following polynomials are irreducible over Z[r].
fi(x) = 17r³ + 7x +3,
f2(x) = 2r* + 3x² +x – 2,
fa(x) = 7x* + 5x – 3.

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