Math Gold Medalist

Lor

2022 AMC 12A 

Problem 21

Let\[P(x) = x^{2022} + x^{1011} + 1.\]Which of the following polynomials is a factor of $P(x)$?

$\textbf{(A)} \, x^2 -x + 1 \qquad\textbf{(B)} \, x^2 + x + 1 \qquad\textbf{(C)} \, x^4 + 1 \qquad\textbf{(D)} \, x^6 - x^3 + 1 \qquad\textbf{(E)} \, x^6 + x^3 + 1$

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   Solution