Hello, i am stumped on these problems, and i am wondering if anybody could help me

1. Prove or disprove that in the ring Z[X], <2X> = <2,X>

2. Suppose that I is an ideal of Q[X] which contains both X^{2} + 2X + 4 and X^{3} - 3. Show that I = Q[X].

3. Prove that in the ring Z[X], <2>U<X> is not an ideal