TR-MO-R1 2019 Problem 7

$P(x) = (x+1)^{2019} + (x-1)^{2019}$ polinomunun $x^2+1$ polinomu ile bölümünden kalan polinom nedir?

a) $2^{2019}x$ b) $2^{1010}x$ c) $2^{1009}x$ d) $2019x$ e) $1010x$

Official text Turkish Mathematical Olympiad, first round 2019 official paper, page 4. Quoted with source.

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