Show that 3x + 4x + 3 E Z,[x] factors as (3x + 2)(x + 4) and (4x + 1)(2x + 3). Explain why this does not contradict the corollary of Theorem 18.3. | Theorem 18.3 PID Implies UFD Every principal ideal domain is a unique factorization domain.
Show that 3x + 4x + 3 E Z,[x] factors as (3x + 2)(x + 4) and (4x + 1)(2x + 3). Explain why this does not contradict the corollary of Theorem 18.3. | Theorem 18.3 PID Implies UFD Every principal ideal domain is a unique factorization domain.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 49PS
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Corollary - Let F be a field. Then F[x] is a unique factorization domain.
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