Answer
$x-2$ is a factor of the given polynomial.
Work Step by Step
The given expression is:-
$(3x^4-6x^3-5x+10)\div (x-2)$
Rewrite as descending powers of $x$.
$(3x^4-6x^3+0x^2-5x+10)\div (x-2)$
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:
$\begin{matrix}
&-- &-- &--&--& -- \\
2) &3&-6&0&-5&10 & \\
& &6 &0 &0 &-10& \\
& -- & -- & --& -- &--& \\
& 3 & 0& 0 &-5 & 0\\
\end{matrix}$
The remainder is $0$.
Hence, $x-2$ is a factor of the given polynomial.
