not numbers, i need the proof.
Let P(x) be a nonzero polynomial such that, for all real numbers x, P(x^2 - 1) = P(x)P(-x). Determine the maximum possible number of real roots of P(x).
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Let P(x) be a nonzero polynomial such that, for all real numbers x, P(x^2 - 1) = P(x)P(-x). Determine the maximum possible number of real roots of P(x).