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Factor f(x) = x¹3-x € Q[x] completely into irreducible factors. Hint: Factor out x first. The remaining factors are irreducible cyclotomic polynomials. Write the irreducible factors in increasing degree.

Factor f(x) = x¹3-x € Q[x] completely into irreducible factors. Hint: Factor out x first. The remaining factors are irreducible cyclotomic polynomials. Write the irreducible factors in increasing degree.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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10 Answer should be x(irred factor 2) (irred factor 3)...(irred factor k) where k is the number of irreducible factors of f. For each cyclotomic polynomial and i<j write i should be written before j for each _n write the actual polynomial in x. Factor f(x) = x¹3-x € Q[x] completely into irreducible factors. Hint: Factor out x first. The remaining factors are irreducible cyclotomic polynomials. Write the irreducible factors in increasing degree.
Transcribed Image Text:10 Answer should be x(irred factor 2) (irred factor 3)...(irred factor k) where k is the number of irreducible factors of f. For each cyclotomic polynomial and i<j write i should be written before j for each _n write the actual polynomial in x. Factor f(x) = x¹3-x € Q[x] completely into irreducible factors. Hint: Factor out x first. The remaining factors are irreducible cyclotomic polynomials. Write the irreducible factors in increasing degree.
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