Answer
$f(3)=240$
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 $x-3$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(x^3+8x^2+29x+82)(x-3)+240$; thus we have $f(3)=240$.
