HMMT November 2010 U24

Let $P(x)$ be a polynomial of degree at most 3 such that $P(x)=\frac{1}{1+x+x^{2}}$ for $x=1,2,3,4$ . What is $P(5)$ ?

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{-3}{91}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.