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4. Find the principal representative of each of the following: x³ -x + 1 mod x + 2 in Q[x] i. x3 ii. x7 + x + 1 mod x3 + x + 1 in Z3[x] iii. x4 + 2x + 4 mod x² + 1 in Z5[x] of Example 5 to find the principal represent

4. Find the principal representative of each of the following: x³ -x + 1 mod x + 2 in Q[x] i. x3 ii. x7 + x + 1 mod x3 + x + 1 in Z3[x] iii. x4 + 2x + 4 mod x² + 1 in Z5[x] of Example 5 to find the principal represent

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(3.7) #4i
**Problem 4:** Find the principal representative of each of the following: i. \( x^3 - x + 1 \mod x + 2 \) in \( \mathbb{Q}[x] \) ii. \( x^7 + x + 1 \mod x^3 + x + 1 \) in \( \mathbb{Z}_3[x] \) iii. \( x^4 + 2x + 4 \mod x^2 + 1 \) in \( \mathbb{Z}_5[x] \)
Transcribed Image Text:**Problem 4:** Find the principal representative of each of the following: i. \( x^3 - x + 1 \mod x + 2 \) in \( \mathbb{Q}[x] \) ii. \( x^7 + x + 1 \mod x^3 + x + 1 \) in \( \mathbb{Z}_3[x] \) iii. \( x^4 + 2x + 4 \mod x^2 + 1 \) in \( \mathbb{Z}_5[x] \)
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