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Applying the multivariate division algorithm by hand, and using graded lexicographic order compute (a) the remainder of f = ry²z? + xy – yz of division by the polynomials {fi = x – y², f2 = y – 23, f3 = z² – 1} given in the order (f1, f2, f3) (b) Repeat part (a) with the order of the dividing polynomials now (f2, f3, f1)- (c) the remainder of f = r3 - a2y – x2z by the polynomials fi = r²y – z and f2 = ry – 1. First find the remainder of division by (f1, f2), then find the remainder of division by (f2; f1). What do you notice?

Applying the multivariate division algorithm by hand, and using graded lexicographic order compute (a) the remainder of f = ry²z? + xy – yz of division by the polynomials {fi = x – y², f2 = y – 23, f3 = z² – 1} given in the order (f1, f2, f3) (b) Repeat part (a) with the order of the dividing polynomials now (f2, f3, f1)- (c) the remainder of f = r3 - a2y – x2z by the polynomials fi = r²y – z and f2 = ry – 1. First find the remainder of division by (f1, f2), then find the remainder of division by (f2; f1). What do you notice?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 26E
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Applying the multivariate division algorithm by hand, and using graded lexicographic order compute (a) the remainder of f = xy2z2 + xy– yz of division by the polynomials {fi = x – y?, f2 = y – 23, f3 = 22 – 1} given in the order (f1, f2: f3) (b) Repeat part (a) with the order of the dividing polynomials now (f2, f3, f1). (c) the remainder of f = x3 – x2y – x2z by the polynomials fi = x?y – z and f2 = ry – 1. First find the remainder of division by (f1, f2), then find the remainder of division by (f2, f1). What do you notice?
Transcribed Image Text:Applying the multivariate division algorithm by hand, and using graded lexicographic order compute (a) the remainder of f = xy2z2 + xy– yz of division by the polynomials {fi = x – y?, f2 = y – 23, f3 = 22 – 1} given in the order (f1, f2: f3) (b) Repeat part (a) with the order of the dividing polynomials now (f2, f3, f1). (c) the remainder of f = x3 – x2y – x2z by the polynomials fi = x?y – z and f2 = ry – 1. First find the remainder of division by (f1, f2), then find the remainder of division by (f2, f1). What do you notice?
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