P for Polynomial

Algebra Level 2

Given that P(x)P(x) is a monic fifth-degree polynomial such that

P(1)=12P(2)=22P(3)=32P(4)=42P(5)=52, \begin{aligned} P(1) & = & 1^2 \\ P(2) & = & 2^2 \\ P(3) & = & 3^2 \\ P(4) & = & 4^2 \\ P(5) & = & 5^2,\end{aligned}

find the value of P(6)P(6).

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