(solution) Use the resolvents given in the text for A 4 , D 4 , and C 4 to determine the isomorphism classes of

(solution) Use the resolvents given in the text for A 4 , D 4 , and C 4 to determine the isomorphism classes of

Use the resolvents given in the text for A 4 , D 4 , and C 4 to determine the isomorphism classes of the Galois groups over Q of the following polynomials. (1) X 4 + 3 X 3 + 4 X 2 + 5 X + 6; (2) X 4 − 8 X 3 + 4 X 2 + 48 X + 16; (3) ( X 3 − 1)( X − 1); (4) ( X 2 − 2) 2 ; (5) X 4 + 2 X 3 − 2 X 2 − 6 X − 3. (Note: Not all of the polynomials are irreducible. What can we say in those cases?)