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-
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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