AMC 10 2025 Part B Problem 10

Let f(n)=n^3-5n^2+2n+8, and let g(n)=n^3-6n^2+5n+12. What is the sum of all integer values of n for which \dfrac{f(n)}{g(n)} is also an integer?

Answer Choices:

A. 2

B. 3

C. 4

D. 5

E. 6