Answer
$f(3)=0$
Work Step by Step
The remainder theorem:
If the polynomial f(x) is divided by $x-c$, then the remainder is $f(c).$
Divide $x^{4}-5x^{3}+5x^{2}+5x-6$
with $x-2,\qquad (c=2)$
$\begin{array}{rrrrrrrr}
\underline{2}| &1 & -5 & 5 & 5 &-6 & & & \\
& & 2 & -6 & -2 & 6 & & & \\
& --& -- &-- &-- & -- & & & \\
&1 & -3 & -1 & 3 & \fbox{0} & & & \end{array}$
Remainder = $f(3)=0$
