Solving Multiplication Tables in Z2[X]/(x^3+x^2+x+1): Steps and Examples

[mikki]

have a question about finding the multiplication table of say
Z2[X]/(x^3+x^2+x+1). What are the steps in solving problems like this? Because I keep doing different problems and I end up making a mistake. All I need is an example or an explanantion. Any help is greatly appreciated

 

[Office_Shredder]

have a question about finding the multiplication table of say
Z2[X]/(x^3+x^2+x+1).

Can you explain the notation? It's not familiar to me

 

[mikki]

the polynomial ring over the integers mod 2: Z2[x]