Calculus or polynomial equations?

Algebra Level pending

\(f(x)\) is a 5-degree polynomial such that \({(x - 1)^3} | f(x) - 1\) and that \({x^3} | f(x)\).

If \(f(x)\) can be expressed as \(a{x}^5 + b{x}^4 + c{x}^3 +d{x}^2 + ex + f\). Find the value of (\(abc)\) .

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