Abstract algebra questions relating to Ideals and cardinality of factor rings

[cloverforce]

Homework Statement

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.

Homework Equations

Can't think of any.

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 \mathbb{Z}_5[x]/I?