I was tutoring yesterday and I got caught completely offguard by this question:

Let $\displaystyle B= \{ 1+t^2,3-t+4t^2,-1+2t-4t^2 \} $

Find $\displaystyle [1-3t+5t^2]_B $ and find q such that [tex]q_B = (1,3,-2)

I forgot most of my linear algebra, and I don't have my notes with me, would anyone please explain this to me? Thanks.