Let $p(x)$ be a quadratic polynomial such that $[p(x)]^3 - x$ is divisible by $(x - 1)(x + 1)(x - 8).$  Find $p(13).$
Question:
Let $p(x)$ be a quadratic polynomial such that $[p(x)]^3 - x$ is divisible by $(x - 1)(x + 1)(x - 8).$  Find $p(13).$
Answer:
Let's think step by step.

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Let $p(x)$ be a quadratic polynomial such that $[p(x)]^3 - x$ is divisible by $(x - 1)(x + 1)(x - 8).$  Find $p(13).$
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