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(Rational Root Theorem) and an 0. Prove that if r and s

Chapter 17, Problem 27E

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QUESTION:

Problem 27E

(Rational Root Theorem)

and an ≠ 0. Prove that if r and s are relatively prime integers and f (r/s) = 0, then r | a0 and s | an.

Questions & Answers

QUESTION:

Problem 27E

(Rational Root Theorem)

and an ≠ 0. Prove that if r and s are relatively prime integers and f (r/s) = 0, then r | a0 and s | an.

ANSWER:

Step 1 of 3

Given  be an element of  such that . Now consider two integers  and  with  such that . We will propose to prove that  and . Now notice that, since  we have

Now notice that

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