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 22E: Let ab in a field F. Show that x+a and x+b are relatively prime in F[x].
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![Let F be an infinite field and let f(x) E F[x]. If fſa) = 0 for infinitely
many elements a of F, show that f(x) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78852faa-8f18-42b0-b7b4-ff9b90f64965%2Fb9330282-5e9b-4285-be9d-cf13838ab270%2Fttzz7cs.jpeg&w=3840&q=75)
Transcribed Image Text:Let F be an infinite field and let f(x) E F[x]. If fſa) = 0 for infinitely
many elements a of F, show that f(x) = 0.
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