# The Galois group of $f(t)=t^3-x_1t^2+x_2t-x_3$

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

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Let $f(t) = (t-a)(t-b)(t-c)$. Expand, and express $x_i$ in terms of $a, b, c$. Under which permutations of $a, b, c$ are these equations still true? –  valtron Jan 11 '13 at 16:26
@valtron 6 permutations? thank you for your comment –  user42912 Jan 11 '13 at 16:53