Let a E Z2 be a zero of the irreducible polynomial x + x + 1 over Z2.Show that the elements of B = {1+a,1+a², 1+ a + a²}are the zeros of x³ + x2 +1 in Z2.

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Answered: Let a E Z2 be a zero of the irreducible…

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 7E

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Let a E Z2 be a zero of the irreducible polynomial x3 + x +1 over Z2. Show that the elements of B = {1+a,1+a², 1+a+a?} are the zeros of x³ + x² + 1 in Z2.