Formal Power Series: Proving ED & Irreducibility in R[x]

[5kold]

Homework Statement

Let F be a field. Consider the ring R=F[[t]] of the formal power series
in t. It is clear that R is a commutative ring with unity.

the things in R are things of the form infiniteSUM{ a_n } = a_0 + a_1 t + a_2 t +...

b is a unit iff the constant term a_0 =/= 0

Prove that R is a Euclidean domain with respect to the norm N(b)=n if a_n is the first term of b that is =/= 0.

In the polynomial ring R[x], prove that x^n-t is irreducible.

The Attempt at a Solution

I showed that it is a ED.

How do I show Irreducibility of this thing?

 

[Nino MMP]

I know that if I can show if the polynomial is reducible, then it can be written as (x^m + k) * (x^n + k2) for some m,k,k2 in R. But how do I prove that this is not the case? Do I use contradiction?