Difference between revisions of "2022 AMC 10B Problems/Problem 21"

(Created page with "==Problem== 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 remai...")
 
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==Video Solution==
 
==Video Solution==
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https://youtu.be/yGUur4vP_6k
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~ 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 22:20, 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)