What does "class $x \in X$ mean?

Question

I'm working through Escofier's book on Galois Theory, and in several exercises regarding finite fields they use the terminology "class $x \in X$, and I'm not certain what it means. For instance, let $K = \mathbb{F}_2[x]/(x^7 + x^3 + 1)$. It's easy to show that $K$ is a field, but then I'm asked to show that "the class $x \in X$ in $K$ generates $K^*$. Is $X$ simply the set of powers of $x$?