Here, we'll provide solutions to a few selected exercises from Chapter 14:
The roots of $f(x)$ are $\sqrt[3]2, \omega\sqrt[3]2, \omega^2\sqrt[3]2$, where $\omega$ is a primitive cube root of unity. The splitting field of $f(x)$ over $\mathbbQ$ is $\mathbbQ(\sqrt[3]2, \omega)$. The Galois group of $f(x)$ over $\mathbbQ$ is isomorphic to $S_3$, the symmetric group on 3 letters. Dummit And Foote Solutions Chapter 14
If you are looking for specific solutions or generated content, these are highly-rated sources: Here, we'll provide solutions to a few selected