In Q[t], define the equivalence relation ~ as f(t) ~ g(t) precisely when f(t) - g(t) is a multiple of t^2 - 5. We define the addition and multiplication of equivalence classes as [f(t)] + [g(t)] = [f(t) + g(t)] and [f(t)] * [g(t)] = [f(t) * g(t)] (Assume: ~ is an equivalence relation, Addition/Mutliplication of equivalence classes is well-defined, and every equivalence class contains exactly one element of the form a + bt, where a, b in Q) a) Find a, b in Q such that [3t^3 - 5t^2 + 8t - 9] = [a + bt] b) Find a, b in Q such that [2t + 7] * [7t + 11] = [a + bt] c) Find two equivalence classes whose square is equal to  d) Find a, b in Q such that [a + bt]^2 + [-2][a + bt] =  (Two possible answers) e) Find a, b in Q such that [2 - t] * [a + bt] =  f) Which equivalence classes are zero divisors? g) Which equivalence classes have multiplicative inverses? h) How many equivalence classes are there whose square is equal to  ? Note: * means multiplication Now, I think I found the following solutions. Can someone verifty these and help solve the remaining parts? a) [35t - 54] b) [71t + 147] c) ?? d) ?? e) ?? f)  = [t^2 - 5] (are these the only zero divisor classes??) g) ?? h) ??