The asymptotic complexity of

\begin{equation*} f(n) = 4n^3 + 3n^2 + 2n + 1 \end{equation*}

in Big O is derived by

\begin{align*} f(n) & = \mathcal{O}(4n^3 + 3n^2 + 2n + 1) \\ & = \mathcal{O}(n^3 + n^2 + n) \\ & = \mathcal{O}(n^3). \end{align*}