Let F be a field and let f(r) = anr" +an-1x"-1+..+ ao € F[x]. Prove that r - 1 is a factor of f(r) if and only if a, + an-1+ ·· ·+ ao = 0. %3D
Let F be a field and let f(r) = anr" +an-1x"-1+..+ ao € F[x]. Prove that r - 1 is a factor of f(r) if and only if a, + an-1+ ·· ·+ ao = 0. %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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![Let F be a field and let f(r) = anr" +an-1x"-1+..+ ao € F[x]. Prove that r - 1 is
a factor of f(r) if and only if a, + an-1+ ·· ·+ ao = 0.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5958936e-64d8-4f9f-ac16-af104f1eb32d%2F12893de3-1416-47ae-98a6-134d6b94f2b7%2Ffganhrs_processed.png&w=3840&q=75)
Transcribed Image Text:Let F be a field and let f(r) = anr" +an-1x"-1+..+ ao € F[x]. Prove that r - 1 is
a factor of f(r) if and only if a, + an-1+ ·· ·+ ao = 0.
%3D
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