Consider the quotient ring R=Z_(2)(x)/(:x^(3)+x+1:). List the elements of this quotient ring and compute the multiplication table. (Here's how to create tables in LaTeX -> ). Determine if R is a field. You may use your table or any of our facts about polynomials. Depending on what you determine in the previous part, do one of the following. Prove your example in either case. If R is a field, give an example of a cubic polynomial f(x)inZ_(2)[x] such that Z_(2)(x)/(:f(x):) is not a field. If R is not a field, give an example of a cubic polynomial f(x)inZ_(2)[x] such that Z_(2)(x)/(:f(x):) is a field