AMC 12 2022a 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 \textbf{(B)} x^2 + x + 1 \textbf{(C)} x^4 + 1 \textbf{(D)} x^6 - x^3 + 1 \textbf{(E)} x^6 + x^3 + 1