Answer
Fill the blanks with
$3\quad ,6\quad $and$\quad 0$
Work Step by Step
We set up polynomial division as
$\text{divisor} )\overline{\text{ dividend }}$,
where the divisor and dividend are polynomials.
When the divisor is a polynomial $(x-a)$ we can use synthetic division.
Here, $a=3$.
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
$(x^{3}+6x^{2}+2x+0)\div(x-3)$
Note that in the dividend, the coefficient next to $x^{0}$ is $0.$
$ \begin{array}{lllllll}
& & -- & -- & -- & -- & \\
\fbox{$3$} & ) & 1 & \fbox{$6$} & 2 & \fbox{$0$} & \\
\hline & & & & & & \\
& & -- & -- & -- & -- & \\
& & & & & &
\end{array} $
Fill the blanks with
$3\quad ,6\quad $and$\quad 0$
