Palindromic Polynomials with Z Module Coefficients

I need to do some research on the properties of palindromic polynomials with Z(n) coefficients.  I would like information/explanation of polynomials with Z(n) coefficients.  I would like to see examples of polynomials with Z(1), Z(2), Z(3), Z(4), Z(5) and in general Z(n) coefficients.  Also, I would like to see some examples of some of these polynomials factored.  

My intent here is to better understand how to construct, investigate and work with a polynomial with coefficients from a set Z(n).  I am seeking a good simple explanation with some good simple examples, so I can do my own calculations and constructing of Z(n) polynomials.  If you can give any palindromic examples and known characteristics of palindromic Z(n) polynomials, that would be great.

I'm just attempting to better understand this type of polynomial before I start to research and work with them.