Is $F_p^{l}[t]$ is a UFD

Question

I'm stuck here.

Let $F_{p}$ be a finite filed. Is $F_{p^{l}}[t]$ a Unique factorization Domain.

Can anyone explain? Thank you very much

Answer 1

I presume $F_{p^l}$ denotes the finite field of order $q^l$.

The polynomial ring $k[t]$ is a UFD for any field $k$. The proof is via the Euclidean algorithm for polynomials.