Show that $3n^3-8n^2+7nlogn-4$ is $(n^3).$ Justify your answer by providing

real$-$valued constant$($s$),$ corresponding to the lower$-$ and upper$-$bound constant factors $c^{\text{'}}$ and

$c^{\text{'}\text{'}},$ respectively, and the integer constant $n_{0}1,$ consistent with the definition of big$-$Theta.

$($Show your work. The provided constants $c^{\text{'}},c^{\text{'}\text{'}},$ and $n_0$ should follow clearly from your work

and be reasonably tight.$)$