Let F be a field of characteristic 3. For a polynomial f e F[X], let f' be the derivative of f. Which of the following maps F(X]F(X] are ring homomorphisms? Select all that apply: O The map f+ f(-1) O The map f+ f' O The map f+f + f' O The map f + f3
Let F be a field of characteristic 3. For a polynomial f e F[X], let f' be the derivative of f. Which of the following maps F(X]F(X] are ring homomorphisms? Select all that apply: O The map f+ f(-1) O The map f+ f' O The map f+f + f' O The map f + f3
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 16E
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![Let F be a field of characteristic 3. For a polynomial f e F[X], let f' be the derivative of f.
Which of the following maps F[X] → F[X] are ring homomorphisms?
Select all that apply:.
O The map f + f(-1)
O The map f + f'
O The map f + f + f'
O The map f + f³](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2faf8876-4d4a-43d8-968a-0cf4e8d21a58%2F2fa699ea-b95b-41d3-9ded-aef5bb1b67f4%2F9tbc32_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let F be a field of characteristic 3. For a polynomial f e F[X], let f' be the derivative of f.
Which of the following maps F[X] → F[X] are ring homomorphisms?
Select all that apply:.
O The map f + f(-1)
O The map f + f'
O The map f + f + f'
O The map f + f³
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