1. Galois group

I'm asked to find the Galois group of this polynomial over Q:
x^5-2x^3-x^2+2.

This is irreducible over Q, but over Fp where p is prime, the polynomial factorises. Does this information help, or is there a different way to find the Galois group?

2. Originally Posted by KSM08
I'm asked to find the Galois group of this polynomial over Q:
x^5-2x^3-x^2+2.

This is irreducible over Q, but over Fp where p is prime, the polynomial factorises. Does this information help, or is there a different way to find the Galois group?

$\displaystyle x^5-2x^3-x^2+2=(x-1)(x^4+x^3-x^2-2x-2)\Longrightarrow$ your polynomial is reducible over $\displaystyle \mathbb{Q}$ .

Tonio