{"status": "success", "data": {"description_md": "Consider the polynomials $P(x)=x^{6}-x^{5}-x^{3}-x^{2}-x$ and $Q(x)=x^{4}-x^{3}-x^{2}-1.$ Given that $z_{1},z_{2},z_{3},$ and $z_{4}$ are the roots of $Q(x)=0,$ find $P(z_{1})+P(z_{2})+P(z_{3})+P(z_{4}).$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Consider the polynomials <span class=\"katex--inline\">P(x)=x^{6}-x^{5}-x^{3}-x^{2}-x</span> and <span class=\"katex--inline\">Q(x)=x^{4}-x^{3}-x^{2}-1.</span> Given that <span class=\"katex--inline\">z_{1},z_{2},z_{3},</span> and <span class=\"katex--inline\">z_{4}</span> are the roots of <span class=\"katex--inline\">Q(x)=0,</span> find <span class=\"katex--inline\">P(z_{1})+P(z_{2})+P(z_{3})+P(z_{4}).</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 4, "problem_name": "2003 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/03_aime_II_p10", "prev": "/problem/03_aime_II_p08"}}