#### FoundBread

##### New member

- Joined
- Aug 1, 2018

- Messages
- 5

Was asked to show that f(x) = x

^{4}+ x

^{3}+ 2x + 1 is irreducible in Z

_{3}[x] which is fine.

But then asked to use a formal root of f(x), α, to describe the finite field F

_{81}.

I think I understand how to construct a field of order 81 by finding an irreducible polynomial of degree 2 over Z

_{9}[X] since 9

^{2}= 81...

But I'm not sure what exactly is meant by using a formal root of f(x) to describe the field.

Any help would be much appreciated,

Thanks