# A Family of Cubics

Algebra Level 4

Let the general cubic polynomial with integer coefficients $$f(x)=ax^3+bx^2+cx+d$$ have the trait that $$f(1)=2k$$ for some integer $$k$$. Does there exist a $$k$$ such that $$f(x)$$ has the factor $$ax^2+(c-d)x+d$$?

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