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Algebra Level 4

Let \(f(x) \) denote a \(10^\text{th} \) degree polynomial such that \(f(x) = 10\) has roots \(x=1,2,3,\ldots,10\) and \(f(x) \) has a constant term of \(10!\). Find \(f(11) \).

Bonus: Generalize this.

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