Determine the gcd of the following pairs of polynomials. a. x* + x +1 and x? + x +1 over GF(2) b. x³ – a +1 and x? +1 over GF(3) c. x° +x* + x³ – x? – x +1 and a + x? +x +1 over GF(3) -

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 17E
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5.9
Determine the gcd of the following pairs of polynomials.
a. x³ + x + 1 and x? + x +1 over GF(2)
b. x³ – x +1 and x? +1 over GF(3)
c. x + x4 + x³ – x² – x+1 and x³ +x² + x + 1 over GF(3)
d. x + 88x4 + 73x³ + 83x² + 51x + 67 and x³ + 97x² +40x + 38 over GF(101)
Transcribed Image Text:5.9 Determine the gcd of the following pairs of polynomials. a. x³ + x + 1 and x? + x +1 over GF(2) b. x³ – x +1 and x? +1 over GF(3) c. x + x4 + x³ – x² – x+1 and x³ +x² + x + 1 over GF(3) d. x + 88x4 + 73x³ + 83x² + 51x + 67 and x³ + 97x² +40x + 38 over GF(101)
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