Recall that m(X) = X + X + 1 € Z2[X] is irreducible. Let K denote the field Z2[X]/(m(X)) and let a denote [X] m(x) € K. (a) For b1, b2, ., bk EK prove the identity (b₁+b2+...+b)² = b² + b²₁₂+ +b². (b) Find the roots of m(X) in K. Express these roots in terms of a. Remark. We know that a Є K is a root of m(X). The problem is to find the rest of the roots or to prove that there are no more roots. (c) Factor m(X) into irreducible polynomials in K[X].

Recall that m(X) = X + X + 1 € Z2[X] is irreducible. Let K denote the field Z2[X]/(m(X)) and let a denote [X] m(x) € K. (a) For b1, b2, ., bk EK prove the identity (b₁+b2+...+b)² = b² + b²₁₂+ +b². (b) Find the roots of m(X) in K. Express these roots in terms of a. Remark. We know that a Є K is a root of m(X). The problem is to find the rest of the roots or to prove that there are no more roots. (c) Factor m(X) into irreducible polynomials in K[X].

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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