{"status": "success", "data": {"description_md": "Let $P(x)$ be a degree $5$ polynomial with a leading coefficient of $1$ and real coefficients. $P(x)$ has complex roots $3+4i$ and $4-i$, and a remainder of $600$ when divided by $(x-1)$. Evaluate $P(2)$.", "description_html": "<p>Let <span class=\"katex--inline\">P(x)</span> be a degree <span class=\"katex--inline\">5</span> polynomial with a leading coefficient of <span class=\"katex--inline\">1</span> and real coefficients. <span class=\"katex--inline\">P(x)</span> has complex roots <span class=\"katex--inline\">3+4i</span> and <span class=\"katex--inline\">4-i</span>, and a remainder of <span class=\"katex--inline\">600</span> when divided by <span class=\"katex--inline\">(x-1)</span>. Evaluate <span class=\"katex--inline\">P(2)</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "TxO Math Bowl 2024 - Individuals A - Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsA-p05", "prev": "/problem/txo2024indivsA-p03"}}