Inspired by Satyajit Mohanty, but this is one is a lot easier!

Algebra Level 4

Let P(x)P(x) be a polynomial such that (x+1)P(x1)=(x1)P(x)(x+1)P(x-1)=(x-1)P(x) for all real values of xx. Determine the maximum possible degree of P(x)P(x).


Inspiration.

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