Let R = Z [x] and let I = <3, x^2 +1> be an ideal. 1) Prove that R/I is isomorphic to Z3 [x]

Let R = Z [x] and let I = be an ideal. 1) Prove that R/I is isomorphic to Z3 [x] / ii) Conclude that R/I is a field and determine the number of its elements, show your steps iii) Prove or show a counterexample: Let S = Z3 [x] / , then the class of x+1 is the multiplicative generator of S* (The Set of the Units of S) RING THEORY (Please prove explicitly all the results and state the theorems used)