Answer
$f(4)=-25$
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 $\{2,-11,7,-5\}$ and the divisor is $x-4$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(2x^2-3x-5)(x-4)-25$; thus we have $f(4)=-25$.
