Answer
$x+3$ is a factor of the given polynomial.
Work Step by Step
The given expression is:-
$(2x^6-18x^4+x^2-9)\div (x+3)$
Rewrite as descending powers of $x$.
$(2x^6+0x^5-18x^4+0x^3+x^2+0x-9)\div (x+3)$
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:
$\begin{matrix}
&-- &-- &--&--& --&--&-- \\
-3) &2&0&-18&0&1 & 0&-9\\
& &-6 &18 &0 &0& -3&9\\
& -- & -- & --& -- &--&--&-- \\
& 2 & -6& 0 &0 & 1&-3&0\\
\end{matrix}$
The remainder is $0$.
Hence, $x+3$ is a factor of the given polynomial.
