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Algebra Level 5

Let \(P(x)\) be a polynomial of degree 99 satisfying \(P(n)=n \cdot 99!\) for \(n= 1,2,3,\ldots,99\). If \(P(100)=0\), find the value of the coefficient of \(x^{98}\) in \(P(x)\).

Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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