Show that is irreducible over , and let be a root of . Compute and .
is Eisenstein at 2, and so is irreducible over .
In , we have . We can easily see that .
Next we compute ; to this end, we use the extended Euclidean Algorithm to find polynomials and in such that ; evidently, and work. (WolframAlpha agrees.) Thus, mod , we have . Now .