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Algebra Level 3

Let f(x)f(x) denote a 10th10^\text{th} -degree polynomial such that f(x)=10f(x) = 10 has roots x=1,2,3,,10x=1,2,3,\ldots,10 and f(x)f(x) has a constant term of 10!10!. Find f(11)f(11) .


Bonus: Generalize this.

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