Exercise
If f 
Q[X],
we usually write Q[f] for the subring of
Q[X] generated by f.
What is the intersection of Q[X2] and Q[X+1]?
Q[X2(X+1)]
Q[X4]
Q
No,
the polynomial X2(X+1) belongs to neither
Q[X2] nor
Q[X+1].
No, the
polynomial X4 does not belong to
Q[X+1].
True. Can you prove it?