Question: i. Show that f(x) = x' + 2x +1 is irreducible in Z3r]. ii. Using a formal root a of f(x) from part (i),

i. Show that f(x) = x' + 2x +1 is irreducible in

i. Show that f(x) = x' + 2x +1 is irreducible in Z3r]. ii. Using a formal root a of f(x) from part (i), describe the finite field Fr. [4 marks) [3 marks] iii. Find (a?+2)-1 in F27. Exprkss your answer in the form of part ii. [7 marks] [6 marks] 6 marks] iv. Solve the equation oX + 20 X for X in F7. v. What is the order of the element a in Fr?

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