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Unformatted text preview: pearing are unique up to multiplication by nonzero elements in K . Proof. Exercise 1.8.9 . n This completes our treatment of unique factorization of polynomials. Before we leave the topic, let us notice that you havent yet learned any general methods for recognizing irreducible polynomials, or for carrying out the factorization of a polynomial by irreducible polynomials. In the integers, you could, at least in principle, test whether a number n is prime, and nd its prime factors if it is composite, by searching for divisors among the natural numbers p n . For an innite eld such as Q , we cannot...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Polynomials

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