Determine Whether Or Not Each Of The Following Polynomials Irreducible

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 + 3×2 – x + 1 over Z5

Posted in Uncategorized