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 haven’t 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 ﬁnd its prime factors if it is composite, by searching for divisors among the natural numbers ² p n . For an inﬁnite ﬁeld such as Q , we cannot...
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 Fall '08
 EVERAGE
 Algebra, Polynomials, Prime number, Greatest common divisor, Proof. Exercise

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