Does anyone know why x^4 + 1 is reducible mod p for any prime. Is this because x^4 + 1 mod 3 has 2*4 + 1 = 9 mod 3 = 0??? Because 0^4 + 1 = 1, 1^4 + 1 = 2, 2^4 + 1 = 17 do not seem to be 0 mod 3.
Irreducibility for degree 4 or higher does not have to have zeros. Ex (x^2 + 1)^2 = x^4 + 2x^2 + 1
