Thank you 1. Let F be a field. Suppose that the polynomial ƒ(x) = F[x] is a unit in the polynomial ring F[x]. Provethat f(x) = a must be a constant polynomial, where a E F is a non-zero element of the field.Hint: Let g(x) = F[x] be the multiplicative inverse of f(x). What can you say about deg f(x) and deg g(x)?

f(x) is a constant polynomial Explanation:Step 1: Step 2: Step 3: Step 4:

Answered: 1. Let F be a field. Suppose that the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 13E

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