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2025 AMC 10B Problem 10

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2025 AMC 10B Problem 10AMC 10 Step by Step
Name:                             Date: September 13, 2026
Polynomials · difficulty 3 of 5 · about 4 min · position P1-10

Let f(n)=n3−5n2+2n+8f(n)=n^3-5n^2+2n+8 and g(n)=n3−6n2+5n+12.g(n)=n^3-6n^2+5n+12. What is the sum of all integers nn such that f(n)g(n)\tfrac{f(n)}{g(n)} is an integer?

  1. A)

    22

  2. B)

    33

  3. C)

    44

  4. D)

    55

  5. E)

    66

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