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
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 13E
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(3.7) #4i
![4. Find the principal representative of each of the following:
− x + 1 mod x +2 in Q[x]
ii. x + x + 1 mod x³ + x +1 in Z3 [x]
.7
i. x³
4
iii. x² + 2x + 4 mod x² + 1 in Z5[x] me bris
qila
5. Use the technique of Example 5 to find the principal representati-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d410cd6-8fc6-4d13-8ff0-7a43ba3056bc%2F27fde0f5-ac8d-45f1-8f1a-99bb51883716%2Fxsf3z85_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Find the principal representative of each of the following:
− x + 1 mod x +2 in Q[x]
ii. x + x + 1 mod x³ + x +1 in Z3 [x]
.7
i. x³
4
iii. x² + 2x + 4 mod x² + 1 in Z5[x] me bris
qila
5. Use the technique of Example 5 to find the principal representati-
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