Answered: Let F be a field and let p(x) ∈ F[x].…

Let F be a field and let p(x) ∈ F[x]. If f(x), g(x) ∈ F[x] anddeg f(x) < deg p(x) and deg g(x) < deg p(x), show that f(x)+<p(x)> = g(x)+ <p(x)> implies f(x) =g(x).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 36E

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Question

Let F be a field and let p(x) ∈ F[x]. If f(x), g(x) ∈ F[x] and
deg f(x) < deg p(x) and deg g(x) < deg p(x), show that f(x)+
<p(x)> = g(x)+ <p(x)> implies f(x) =g(x).

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