Using the Roots of a Polynomial

Calculus Level 5

What is the smallest degree of a non-constant complex polynomial f(x)f(x), such that the only roots of ff are 00, 22 and 33, and the derivative of f(x)f(x) is divisible by 8x224x+78x^2-24x+7?

Details and assumptions

All roots of f(x)f(x), real or complex, are in the set {0,2,3}\{0,2,3\}.

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