Let $P(x)$ be a polynomial such that
\[P(x) = P(0) + P(1) x + P(2) x^2\]and $P(-1) = 1.$  Find $P(x).$
Question:
Let $P(x)$ be a polynomial such that
\[P(x) = P(0) + P(1) x + P(2) x^2\]and $P(-1) = 1.$  Find $P(x).$
Answer:
Let's think step by step.

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x^2 - x - 1
Let $P(x)$ be a polynomial such that
\[P(x) = P(0) + P(1) x + P(2) x^2\]and $P(-1) = 1.$  Find $P(x).$
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