Abstract Algebra: Theory and Applications · Problem 17.5.8

Integral Domains — Thomas Judson

Mathematics — Abstract Algebra · irreducible-polynomials

Problem

Which of the following polynomials are irreducible over Q[x]\mathbb{Q}[x]? ((a)) x4−2x3+2x2+x+4x^4 - 2x^3 + 2x^2 + x + 4 ((b)) x4−5x3+3x−2x^4 - 5x^3 + 3x - 2 ((c)) 3x5−4x3−6x2+63x^5 - 4x^3 - 6x^2 + 6 ((d)) 5x5−6x4−3x2+9x−155x^5 - 6x^4 - 3x^2 + 9x - 15 Hint. (a) Reducible; (c) irreducible.

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