How can I show that the Galois group of the polynomail f(x) over rationals is S_5.

f(x) = x^6-20x^5+220x^4-1120x^3+2800x^2-13392x+1600.

my hint says that splitting field of f is contained in the splitting field of x^5+2x+2 over rationals.

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- April 11th 2009, 10:39 AMpeteryellowGalois Theory
How can I show that the Galois group of the polynomail f(x) over rationals is S_5.

f(x) = x^6-20x^5+220x^4-1120x^3+2800x^2-13392x+1600.

my hint says that splitting field of f is contained in the splitting field of x^5+2x+2 over rationals.