Problem #PRU-64410

Problems Calculus Derivative Derivative and multiple roots

Problem

Prove that for $n > 0$ the polynomial $P (x) = n^{2} x^{n + 2} - (2 n^{2} + 2 n - 1) x^{n + 1} + (n + 1)^{2} x^{n} - x - 1$ is divisible by $(x - 1)^{3}$ .

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