Answer
$x-2$ is not a factor of the given polynomial.
Work Step by Step
The given expression is:-
$(4x^3-3x^2-8x+4)\div (x-2)$
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 synhtetic division to obtain:
$\begin{matrix}
&-- &-- &--&--&& \\
2) &4&-3&-8&4&&& \\
& &8 &10 &4 & &\\
& -- & -- & --&-- &&& \\
& 4 & 5 & 2 & 8 &&\\
\end{matrix}$
The Remainder is not zero.
Hence, $x-2$ is not a factor of the given polynomial.
