Suppose K[x] splits in F as = (x - u 1 ) n1

Suppose ∫ ϵ K[x] splits in F as ∫ = (x - u₁)ⁿ¹ • • • (x - u_k)^nk (u_i distinct; n_i ≥ 1). Let v₀ , ••• , v_k be the coefficients of the polynomial g = (x - u₁)(.x - u₂) ••• (x - u_k) and let E = K(v₀ , ••• v_k). Then 

(a) F is a splitting field of g over E.

(b) F is Galois over E.

(c) Aut_EF = Aut_KF.