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(b) Consider f(x) = 2x³ + 3x² + 4 in Zs [], 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 Z5 [] completely. (Ctrl) -

(b) Consider f(x) = 2x³ + 3x² + 4 in Zs [], 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 Z5 [] completely. (Ctrl) -

Advanced Engineering Mathematics
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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(b) Consider f(x) = 2x³ + 3x² + 4 in Z₁ [], 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 Z5 [] completely. (Ctrl) ▼ Accessibility: Investigate O i P 6 a hp D'Focus 1316 11011 39°F A
Transcribed Image Text:(b) Consider f(x) = 2x³ + 3x² + 4 in Z₁ [], 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 Z5 [] completely. (Ctrl) ▼ Accessibility: Investigate O i P 6 a hp D'Focus 1316 11011 39°F A
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