{"status": "success", "data": {"description_md": "Let $P(x)$ be a polynomial with rational coefficients such that when $P(x)$ is divided by the polynomial $x^2 + x + 1$, the remainder is $x + 2$, and when $P(x)$ is divided by the polynomial $x^2 + 1$, the remainder is $2x + 1$. There is a unique polynomial of least degree with these two properties. What is the sum of the squares of the coefficients of that polynomial?\n\n$\\textbf{(A) } 10 \\qquad \\textbf{(B) } 13 \\qquad \\textbf{(C) } 19 \\qquad \\textbf{(D) } 20 \\qquad \\textbf{(E) } 23$", "description_html": "

Let P(x) be a polynomial with rational coefficients such that when P(x) is divided by the polynomial x^2 + x + 1 , the remainder is x + 2 , and when P(x) is divided by the polynomial x^2 + 1 , the remainder is 2x + 1 . There is a unique polynomial of least degree with these two properties. What is the sum of the squares of the coefficients of that polynomial?

\n

\\textbf{(A) } 10 \\qquad \\textbf{(B) } 13 \\qquad \\textbf{(C) } 19 \\qquad \\textbf{(D) } 20 \\qquad \\textbf{(E) } 23

\n

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2022 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10B_p22", "prev": "/problem/22_amc10B_p20"}}