Answer
$f(3)=240$
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 $x-3,\qquad (c=3)$
$\begin{array}{rrrrrrrr}
\underline{3}| &1 & 5 & 5 & -5 &-6 & & & \\
& & 3 & 24 & 87 & 246 & & & \\
& --& -- &-- &-- & -- & & & \\
&1 & 8 & 29 & 82 & \fbox{240} & & & \end{array}$
Remainder = $f(3)=240$
