Answer
$Q(x)=x^{4}+x^{3}+4x^{2}+4x+4,\quad R(x)=-2$
Work Step by Step
Important: zeros for missing powers of P(x).
$\left.\begin{array}{l}
1 \ \lfloor \\ \\ \\ \end{array}\right.\begin{array}{rrrrr}
1 & 0 & 3 & 0 & 0 & -6 \\\hline
& 1 & 1 & 4 & 4 & 4 \\\hline
1 & 1 & 4 & 4 & 4 &|\ \ \ -2 \end{array}$
$Q(x)=x^{4}+x^{3}+4x^{2}+4x+4,\quad R(x)=-2$
