Answer
$f(-2)=-4$
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 $\{4,5,-6,-4\}$ 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 $f(x)=(4x^2-3x)(x+2)-4$; thus we have $f(-2)=-4$.
