4. Let f(x), g(x) Q[x] be solvable by radicals. Show that fg is solvable by radicals. Hint : Let E, F, F0 be the splitting fields of fg, f, g, over Q, respectively. So F, F0 are subfields of E. Show that Gal(E/Q) = Gal(F/Q)Gal(F 0/Q).

Let f(x), g(r) ( Q[x] be solvable by radicals. Show that fy is solvable by radicals. Hint : Let E, F. F' be the splitting fields of fg, f, g, over Q, respectively. So F, F' are subfields of E. Show that Gal( E/Q) ~ Gal( F/Q) x Gal(F'/Q)