Answered: Suppose that f(x)=xn+an-1xn-1+...+a0 is…

Suppose that f(x)=xn+an-1xn-1+...+a0 is an element in Z[x]. If r is rational and x-r divides f(x), prove that r is an integer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.4: Complex And Rational Zeros Of Polynomials

Problem 38E

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Suppose that f(x)=xⁿ+a_n-1x^n-1+...+a0 is an element in Z[x]. If r is rational and x-r divides f(x), prove that r is an integer.

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