{"status": "success", "data": {"description_md": "Let $f(x)$ be a polynomial with real coefficients such that $f(0) = 1,$ $f(2)+f(3)=125,$ and for all $x$, $f(x)f(2x^{2})=f(2x^{3}+x).$ Find $f(5).$\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>Let <span class=\"katex--inline\">f(x)</span> be a polynomial with real coefficients such that <span class=\"katex--inline\">f(0) = 1,</span> <span class=\"katex--inline\">f(2)+f(3)=125,</span> and for all <span class=\"katex--inline\">x</span>, <span class=\"katex--inline\">f(x)f(2x^{2})=f(2x^{3}+x).</span> Find <span class=\"katex--inline\">f(5).</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": 6, "problem_name": "2007 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/07_aime_II_p15", "prev": "/problem/07_aime_II_p13"}}