{"status": "success", "data": {"description_md": "Let $P(x) = (x - 1)(x - 2)(x - 3)$. For how many polynomials $Q(x)$ does there exist a polynomial $R(x)$ of degree 3 such that $P(Q(x)) = P(x) \\cdot R(x)$?\n\n$\\mathrm {(A) } 19 \\qquad \\mathrm {(B) } 22 \\qquad \\mathrm {(C) } 24 \\qquad \\mathrm {(D) } 27 \\qquad \\mathrm {(E) } 32$\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--inline\">P(x) = (x - 1)(x - 2)(x - 3)</span> . For how many polynomials  <span class=\"katex--inline\">Q(x)</span>  does there exist a polynomial  <span class=\"katex--inline\">R(x)</span>  of degree 3 such that  <span class=\"katex--inline\">P(Q(x)) = P(x) \\cdot R(x)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A) } 19 \\qquad \\mathrm {(B) } 22 \\qquad \\mathrm {(C) } 24 \\qquad \\mathrm {(D) } 27 \\qquad \\mathrm {(E) } 32</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": "2005 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12A_p25", "prev": "/problem/05_amc12A_p23"}}