How do you use synthetic division to divide (-3x^4)/(x+2)?

$\frac{- 3 {x}^{4}}{x + 2} = - 3 {x}^{3} + 6 {x}^{2} - 12 x + 24$ with a Remainder of $\left(- 48\right)$
$\left(x + 2\right) = 0 \rightarrow x = \textcolor{red}{\left(- 2\right)}$
Synthetic division by $\left(x + 2\right)$ is equivalent to synthetic substitution with $x = \textcolor{red}{\left(- 2\right)}$
{:(,,color(grey)x^4,color(grey)x^3,color(white)("xx")color(grey)x^2,color(white)("x")color(grey)x^1,color(white)("xx")color(grey)x^0), (," | ",-3,0,color(white)("xx")0,color(white)("x")0,color(white)("xx")0), (ul(+color(white)("x"))," | ",ul(color(white)("Xx")),ul(6),ul(-12),ul(24),ul(-48)), (xxcolor(red)((-2))," | ",-3,6,-12,24,-48), (,,color(grey)(x^3),color(grey)(x^2),color(white)("x")color(grey)(x^1),color(grey)(x^0),color(grey)R) :}