Answer
Fill the blanks with
$-2\quad$and$\quad 0$
Work Step by Step
We usually set up division as
divisor $)\overline{\text{ dividend }}$
The divisor and dividend can be polynomials, in which case we perform polynomial division.
When the divisor is a polynomial $(x-a)$ we can use synthetic division.
Here, $a=-2$.
With synthetic division,
in the divisor placeholder, we place $a,$
and in the dividend, we list ALL coefficients (including the zeros ), starting from highest power of x.
The polynomial division here is
$(x^{3}+4x+2)\div(x+2)$
Note that in the dividend,
the coefficient next to $x^{2}$ is $0.$
$ \begin{array}{lllllll}
& & -- & -- & -- & -- & \\
\fbox{$-2$} & ) & \ {1} & \fbox{$0$} & 4 & 2 & \\
\hline & & & & & & \\
& & -- & -- & -- & -- & \\
& & & & & &
\end{array} $
Fill the blanks with
$-2\quad$and$\quad 0$
