# Successive Cubic Rational Root

Algebra Level pending

Let $$f(x) = ax^3 + bx^2 + cx + d$$ where $$c$$ and $$a$$ and $$f(1)$$ are successive positive integers, or $$0 < c < a=2k < f(1)$$ for some integer $$k$$. Find $$d$$ such that $$f(x) = (ax + d)[x^2 + (c-ad)x +d]$$.

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