Let f(x), g(x) be in F(x). Show that if g(x)|f(x) and f(x)|g(x), then f(x)=kg(x) for some k in F.
Since g(x)|f(x), then f(x)=g(x)r(x) for some r(x) in F(x).
Similarily, since f(x)|g(x), then g(x)=f(x)s(x)
So f(x)=f(x)s(x)r(x)
I don't know where to go from here.