Construction of $\GF(p^n)$ as $\FF_p[x]/(f)$

An irreducible degree-$n$ polynomial over $\FF_p$ presents the field with $p^n$ elements.Suggest a slogan

Let $p$ be a prime, $n\geq 1$, and $f \in \FF_p[x]$ an irreducible polynomial of degree $n$, and let $\alpha$ be a root of $f$ in an extension field of $\FF_p$. Then \[ \GF(p^n)\cong \frac{\FF_p[x]}{(f)} \cong \FF_p[\alpha] = \spanof_{\FF_p}\theset{1, \alpha, \ldots, \alpha^{n-1}}. \]