Compare the coefficients

Algebra Level 3

Suppose the polynomials \(P_1(x)\) and \(P_2(x)\) are obtained by expanding and simplifying the following algebraic expressions

\[P_1(1) = (1 + x^2 - x^5)^{2000} \\ P_2(x) = (1 - x^2 + x^5)^{2000}.\]

Let \(C_1\) and \(C_2\) be the coefficient of \(x^{800}\) in the polynomials \(P_1(x)\) and \(P_2(x)\) respectively. Which of the given option is true?

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