(b) Consider f(x) = 2x³ + 3x² + 4 in Z[], and the evaluation homomorphism 2 [2] : Z₁ [2] → Zg. (i) Determine whether f(x) is in the kernel of 2. (ii) Determine whether - 2 is a factor of f(x). (iii) Factor f(x) in Z₁ [] completely. (Ctrl) - Abstract Algebra part iii only...I was able to find 2 zeros being 3 and 4 when checking elements in Z_5 but from there got stuck
(b) Consider f(x) = 2x³ + 3x² + 4 in Z[], and the evaluation homomorphism 2 [2] : Z₁ [2] → Zg. (i) Determine whether f(x) is in the kernel of 2. (ii) Determine whether - 2 is a factor of f(x). (iii) Factor f(x) in Z₁ [] completely. (Ctrl) - Abstract Algebra part iii only...I was able to find 2 zeros being 3 and 4 when checking elements in Z_5 but from there got stuck
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Abstract Algebra
![1:34
air GH .
NO 5GE
← Expert Q&A
(b) Consider ƒ(z) = 2x³ + 3x² + 4 in Z₁ [™], and the evaluation homomorphism
2[2]: Zs [2] → Zg.
(i) Determine whether f(x) is in the kernel of 2.
(ii) Determine whether - 2 is a factor of f(x).
(iii) Factor f(x) in Z[] completely.
(Ctrl) -
Abstract Algebra part iii only...I was able to find
2 zeros being 3 and 4 when checking elements
in Z_5 but from there got stuck
88
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Transcribed Image Text:1:34
air GH .
NO 5GE
← Expert Q&A
(b) Consider ƒ(z) = 2x³ + 3x² + 4 in Z₁ [™], and the evaluation homomorphism
2[2]: Zs [2] → Zg.
(i) Determine whether f(x) is in the kernel of 2.
(ii) Determine whether - 2 is a factor of f(x).
(iii) Factor f(x) in Z[] completely.
(Ctrl) -
Abstract Algebra part iii only...I was able to find
2 zeros being 3 and 4 when checking elements
in Z_5 but from there got stuck
88
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