Answer
$f(2)=0$
Work Step by Step
Step 1. Based on the Remainder Theorem, the value of $f(c)$ can be obtained as the remainder of $f(x)$ divided by $x-c$.
Step 2. The coefficients of the dividend $f(x)$ can be identified in order as $\{1,-5,5,5,-6\}$ and the divisor is $x-2$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(x^3-3x^2-x+3)(x-2)+0$; thus we have $f(2)=0$.
