Abstract algebra questions relating to Ideals and cardinality of factor rings

cloverforce

1. The problem statement, all variables and given/known data
Find the number of elements in the ring Z_5[x]/I, where I is a) the ideal generated by x^4+4, and b) where I is the ideal generated by x^4+4 and x^2+3x+1.


2. Relevant equations
Can't think of any.


3. The attempt at a solution
I started by finding the zeros of the generating polynomial for part a (which are 1, 2, 3, and 4 in Z_5), but I'm not even sure if that helps. This problem is from a list of practice problems for a test, but they're all of a type which we haven't covered in class, and I can't find any reference to anything like this in my textbook.

micromass

Can you describe or list the elements in [tex]\mathbb{Z}_5[x]/I[/tex]?