(Solution) - Determine whether or not each of the following polynomials irreducible -(2025 Original AI-Free Solution)

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Determine whether or not each of the following polynomials irreducible over the given fields. If it is reducible, provide factorization into irreducible factors.
(a) x2 + 3x - 1 over Q, R, C
(b) x4 - 2 over Q, R, C
(c) x2 + x + 1 over Z3, Z5, Z7
(d) x4 + x3 + 1 over Z2
(e) x3 + 3x2 - x + 1 over Z5