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Just had an exam where the last question was:

Find a basis for the subset of $\mathbb{P}_3$ where $p(1) = 0$ for all $p$.

I answered $\{t,t^2-1,t^3-1\}$, but I'm not entirely confident in the answer. Did I think about the question in the wrong way?

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    Your first polynomial, $t$, isn’t in the subspace: if if $p(t)=t$, then $p(1)=1$, not $0$. Did you mean $t-1$? That would work.2012-11-15
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    Since you have only told us your answer, and haven't told us how you thought about the question, it is impossible to answer your query as to whether you thought about the question the wrong way.2012-11-16

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