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> Let $W$ be a subspace of the polynomials with maximum degree of $3$ and $p(1) = p(2) = 0$. Find the basis and the dimension of the subspace. The field is the real numbers.
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My attempt:

My first thought is that it is the usual basis of $\mathbb{P}\_3 = \{1, x, x^2, x^3\}$. However, on second thought, is it a trick question? We will never have $p(1) = p(2)$, will we? So would the basis be the empty set and the dimension be $0$?