Let F be a field, and p(x) E F[x] an irreducible polynomial of degree od. Prove that every coset of Flr]/(p) can be represented by a unique polyno- mial of degree strictly less than d, and moreover that these are all distinct. Prove that if F has q elements, F[x]/(p) has q elements. has ql elements.

Let F be a field, and p(x) E F[x] an irreducible polynomial of degree od. Prove that every coset of Flr]/(p) can be represented by a unique polyno- mial of degree strictly less than d, and moreover that these are all distinct. Prove that if F has q elements, F[x]/(p) has q elements. has ql elements.

Name: Abstract Algebra. Please explain everything in detail. Let F be a fiel
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Description: Abstract Algebra. Please explain everything in detail. Let F be a field, and p(x) E F[x] an irreducible polynomial of degree od.Prove that every coset of Flr]/(p) can be represented by a unique polyno-mial of degree strictly less than d, and moreover

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 10E

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