Difference between revisions of "2022 AMC 12B Problems/Problem 20"

Latest revision as of 23:21, 4 January 2023

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-== Problem ==
+#redirect [[2022 AMC 10B Problems/Problem 21]]
-Let <math>P(x)</math> be a polynomial with rational coefficients such that when <math>P(x)</math> is divided by the polynomial <math>x^2+x+1</math>, the remainder is <math>x+2</math>, and when <math>P(x)</math> is divided by the polynomial <math>x^2+1</math>, the remainder is <math>2x+1</math>. 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?
-<math>\textbf{(A)}\ 10 \qquad
-\textbf{(B)}\ 13 \qquad
-\textbf{(C)}\ 19 \qquad
-\textbf{(D)}\ 20 \qquad
-\textbf{(E)}\ 23 \qquad</math>