(a) Consider the extension Q(u) of Q generated by a real root u of x³ - 6x²+ 9x + 3. (Why is this irreducible?) Express each of the following elements in terms of the basis {1,u,u² } : u⁴ ;u⁵ ;3u⁵ - u^4|+ 2; (u + 1)^-1; (u² - 6u + 8)^-1•

(b) Do the same with respect to the basis { 1,u,u²,u³ ,u⁴} of Q(u) where u is a real root of x⁵ + 2x + 2 and the elements in question are: (u² + 2)(u³ + 3u);u^-1; u⁴(u⁴ + 3u² + 7u + 5);(u + 2)(u2 + 3)^-1•