Answered: Suppose that f(x) = xn +…

Suppose that f(x) = xn + a(n-1)x(n-1)+...+ a0 is an element of 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

Section4.2: Properties Of Division

Problem 51E

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Question

Suppose that f(x) = xⁿ + a_(n-1)x^(n-1)+...+ a₀ is an element of Z[x].

If r is rational and x - r divides f(x), prove that r is an integer.

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