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

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