{"status": "success", "data": {"description_md": "Let $$P(x) = x^{2022} + x^{1011} + 1.$$ Which of the following polynomials is a factor of $P(x)$?\n\n$\\textbf{(A)} \\, x^2 -x + 1 \\qquad\\textbf{(B)} \\, x^2 + x + 1 \\qquad\\textbf{(C)} \\, x^4 + 1 \\qquad\\textbf{(D)} \\, x^6 - x^3 + 1  \\qquad\\textbf{(E)} \\, x^6 + x^3 + 1$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--display\">P(x) = x^{2022} + x^{1011} + 1.</span>  Which of the following polynomials is a factor of  <span class=\"katex--inline\">P(x)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\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</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2022 AMC 12A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12A_p22", "prev": "/problem/22_amc12A_p20"}}