Given a field F, let f(x) F[x] where f(x) = anxn + an-1xn-l +

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Given a field F, let f(x) ∈ F[x] where f(x) = anxn + an-1xn-l + • • • + a2x2 + a1x + do. Prove that x - 1 is a factor of f(x) if and only if
an + an - l + ∙∙∙∙∙∙∙ + a2 + a1 + a0 = 0.

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Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

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Question Posted: Jun 21, 2016 09:12 AM

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Given a field F, let f(x) F[x] where f(x) = anxn + an-1xn-l +

Question:

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a If x 1 is a factor of x then 1 is a root of the polynomial Consequently 0 fl ...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

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