# I don't know how to count

Algebra Level 4

Consider a quintic function $$f(x)$$ such that $$f(k) = k$$ for $$k=1,2,3,4,5$$. Given that $$f(x) = g(x) + q(x)$$ such that $$g(x)$$ has all real roots and its leading coefficient is an integer and $$q(x)$$ is a linear function, which of these answer choices is $$(f(6) - 6)$$ always divisible by?

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