Answer
$x-2$ is a factor of the given polynomial.
Work Step by Step
The given expression is:-
$(4x^4-15x^2-4)\div (x-2)$
Rewrite as descending powers of $x$.
$(4x^4+0x^3-15x^2+0x-4)\div (x-2)$
The divisor is $x-2$, so the value of $c=2$.
and on the right side the coefficients of dividend in descending powers of $x$.
Perform synthetic division to obtain:
$\begin{matrix}
&-- &-- &--&--& -- \\
2) &4&0&-15&0&-4 & \\
& &8 &16 &2 &4& \\
& -- & -- & --& -- &--& \\
& 4 & 8& 1 &2 & 0\\
\end{matrix}$
The remainder is $0$.
Hence, $x-2$ is a factor of the given polynomial.
