AMC 10 Step by Step
Log inSign up
Printable

2010 AMC 10B Problem 25

Include the solutionBack to the problem
2010 AMC 10B Problem 25AMC 10 Step by Step
Name:                             Date: September 13, 2026
Polynomials · difficulty 5 of 5 · about 10 min · position P21-25

Let a>0a > 0 , and let P(x)P(x) be a polynomial with integer coefficients such that

P(1)=P(3)=P(5)=P(7)=aP(1) = P(3) = P(5) = P(7) = a , and
P(2)=P(4)=P(6)=P(8)=−aP(2) = P(4) = P(6) = P(8) = -a .

What is the smallest possible value of aa ?

  1. A)

    105105

  2. B)

    315315

  3. C)

    945945

  4. D)

    7!7!

  5. E)

    8!8!

Working