Answer
$5x^{2}+ 3x - 2$
Work Step by Step
Since we are dividing by (x + 3) the zero of that x = -3 goes into the top left space.
$\hspace{0mm}\underline{-3|}\hspace{5mm}5\hspace{5mm}18\hspace{5mm}7\hspace{5mm}-6$
$ \hspace{15mm}\underline{-15\hspace{1mm}-9\hspace{10mm}6}$
$\hspace{11mm}5\hspace{7mm}3\hspace{3mm}-2\hspace{7mm}\underline{|0}$
Since the bottom right space has a 0, there is no reminder.
