the blank: 1. Let F be a field equipped with a Euclidean valuation δ: D\{0} → N∪{0} defined by δ(f)=deg f. If δ(f)=0 then f(x) must be a ____. 2. Let f and g be nonzero polynomials in F[x]. Then the unique greatest common divisor of f and g is the polynomial p that divides both f and g such that p is ____ and of ____. 3. Let F[x] be the ring of polynomials with coefficients over a field F. We say that p is an irreducible polynomial in F[x] iff deg p > 0 and the factors of p must be a unit and its _____.

the blank: 1. Let F be a field equipped with a Euclidean valuation δ: D\{0} → N∪{0} defined by δ(f)=deg f. If δ(f)=0 then f(x) must be a . 2. Let f and g be nonzero polynomials in F[x]. Then the unique greatest common divisor of f and g is the polynomial p that divides both f and g such that p is and of . 3. Let F[x] be the ring of polynomials with coefficients over a field F. We say that p is an irreducible polynomial in F[x] iff deg p > 0 and the factors of p must be a unit and its _.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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