An algebra problem by Justin Tuazon

Algebra Level 4

Let \(P(x)\) be a polynomial with a degree of 6. \(P(x)\) satisfies the following conditions: \[ \begin{cases} P(0)=5041 \\ P(1)=3 \\ P(2)=7 \\ P(3)=13 \\ P(4)=21 \\ P(5)=31 \\ P(6)=43 \\ \end{cases} \]

Find the sum of the digits of the value of \(P(9)\).

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