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| == Problem ==
| | #redirect [[2022 AMC 10B Problems/Problem 21]] |
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| 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?
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| <math>\textbf{(A)}\ 10 \qquad
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| \textbf{(B)}\ 13 \qquad
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| \textbf{(C)}\ 19 \qquad
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| \textbf{(D)}\ 20 \qquad
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| \textbf{(E)}\ 23 \qquad</math>
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| == Video Solution by OmegaLearn Using Polynomial Remainders ==
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| https://youtu.be/HdrbPiZHim0
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| ~ pi_is_3.14
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| == See Also ==
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| {{AMC12 box|year=2022|ab=B|num-b=19|num-a=21}}
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| {{MAA Notice}}
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