Find a basis of the linear space and thus determine the dimension.

Where q is a subset of Q_2: all polynomials of degree less than or equal to 2. I had to change it from p to q so the forum didn't make it a smiley...

I'm not sure what to do here. I created an arbitrary form of q(t) and q'(t) and found a basis for each of these.

Now I'm lost, and I'm pretty certain I was never on the right track. Any help would be extremely appreciated.

Thanks.