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Splitting Fields : Find the splitting fields over Q for x^3+3x^2+3x-4.

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Find the splitting fields over Q for x^3+3x^2+3x-4.

Recall a splitting field is as follows: Let K be a field and let
f(x)=a_0+a_1*x+...+a_n*x^n be a polynomial in K[x] of degree n>0. An extension field F of K is called a splitting field for f(x) over K if there exist elements
r_1,r_2,...,r_n elements of F such that (i) f(x)=a_n(x-r_1)(x-r_2)...(x-r_n) and
(ii) F=K(r_1,r_2,...,r_n).

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