Answer
$x+4$ is a factor of the given polynomial.
Work Step by Step
The given expression is:-
$(x^6-16x^4+x^2-16)\div (x+4)$
Rewrite as descending powers of $x$.
$(x^6+0x^5-16x^4+0x^3+x^2+0x-16)\div (x+4)$
The divisor is $x+4$, so the value of $c=-4$.
and on the right side the coefficients of dividend in descending powers of $x$.
Perform synthetic division to obtain:
$\begin{matrix}
&-- &-- &--&--& --&--&-- \\
-4) &1&0&-16&0&1 & 0&-16\\
& &-4 &16 &0 &0& -4&16\\
& -- & -- & --& -- &--&--&-- \\
& 1 & -4& 0 &0 & 1&-4&0\\
\end{matrix}$
The remainder is $0$.
Hence, $x+4$ is a factor of the given polynomial.
