I am trying to figure out if the polynomial [(x^4)+1] is reducible over Z5 and also over Z.
For Z5, i tried:
f(0) = 1
F(1) = 2 = f(2) = f(3) = f(4)
Since neither are zero, i tried
f(x) = (ax^2 + bx + c)(dx^2 + ex + f)
I compared the coefficients but am unable to solve it.
For Z, i...