Rewrite

$\displaystyle \frac{{-{4}{x}^{{3}}-{24}{x}^{{2}}-{30}{x}-{14}}}{{{x}^{{2}}+{5}{x}+{3}}}$

in the form

$\displaystyle {q}{\left({x}\right)}+\frac{{{r}{\left({x}\right)}}}{{{x}^{{2}}+{5}{x}+{3}}}$.

$\displaystyle -{4}{x}^{{3}}-{24}{x}^{{2}}-{30}{x}-{14}$	$\displaystyle =$		$\displaystyle +$
$\displaystyle {x}^{{2}}+{5}{x}+{3}$				$\displaystyle {x}^{{2}}+{5}{x}+{3}$