Difference between revisions of "2005 AMC 12A Problems/Problem 24"

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== Problem ==
 
== Problem ==
Let <math>P(x)=(x-1)(x-2)(x-3)</math>. For how many polynomials <math>Q(x)</math> does there exist a polynomial <math>R(x)</math> of degree 3 such that <math>P(Q(x))=P(x)* R(x)</math>?
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Let <math>P(x)=(x-1)(x-2)(x-3)</math>. For how many [[polynomial]]s <math>Q(x)</math> does there exist a polynomial <math>R(x)</math> of degree 3 such that <math>P(Q(x))=P(x)* R(x)</math>?
  
 
== Solution ==
 
== Solution ==

Revision as of 09:16, 9 September 2007

Problem

Let $P(x)=(x-1)(x-2)(x-3)$. For how many polynomials $Q(x)$ does there exist a polynomial $R(x)$ of degree 3 such that $P(Q(x))=P(x)* R(x)$?

Solution

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See also