Answer
$x+3$ is a factor of the given polynomial.
Work Step by Step
The given expression is:-
$(3x^6+82x^3+27)\div (x+3)$
Rewrite as descending powers of $x$.
$(3x^6+0x^5+0x^4+82x^3+0x^2+0x+27)\div (x+3)$
The divisor is $x+3$, so the value of $c=-3$.
and on the right side the coefficients of dividend in descending powers of $x$.
Perform synthetic division to obtain:
$\begin{matrix}
&-- &-- &--&--& --&--&-- \\
-3) &3&0&0&82&0 & 0&27\\
& &-9 &27 &-81 &-3& 9&-27\\
& -- & -- & --& -- &--&--&-- \\
& 3 & -9& 27 &1 & -3&9&0\\
\end{matrix}$
The remainder is $0$.
Hence, $x+3$ is a factor of the given polynomial.
