Art of Problem Solving

2022 AMC 10B Problems/Problem 21: Difference between revisions

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==Video Solution==
==Video Solution==
https://youtu.be/yGUur4vP_6k
~ ThePuzzlr


https://youtu.be/ELdhkqVyB9E
https://youtu.be/ELdhkqVyB9E


~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)

Revision as of 21:20, 17 November 2022

Problem

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?

Video Solution

https://youtu.be/yGUur4vP_6k

~ ThePuzzlr

https://youtu.be/ELdhkqVyB9E

~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)