I'm trying to solve this question:
Let $F[x_1, x_2,x_3]$ be a polynomial ring in $x_1, x_2,x_3$ over a field $F$.
Let $K=F(x_1,x_2,x_3)$ be the field of rational functions (i.e., the field of fractions of the ring $F[x_1,x_2,x_3])$. Suppose $f(t)=t^3-x_1t^2+x_2t-x_3 \in K[t]$. Prove that the Galois group of $f(t)$ over $K$ is $S_3$.
Generalize this result to a polynomial of degree $n$
I'm trying to do the first part of this question, but I have no idea how to begin, I need a hint or something to begin to solve the problem. Any help is welcome!
Thanks a lot