Answer
$f(-2)=-4$
Work Step by Step
The remainder theorem:
If the polynomial f(x) is divided by $x-c$, then the remainder is $f(c).$
Divide $4x^{3}+5x^{2}-6x-4$
with $x+2,\qquad (c=-2)$
$\begin{array}{rrrrrrrr}
\underline{-2}| &4 & 5 & -6 & -4 & & & & \\
& & -8 & 6 & 0 & & & & \\
& --& -- &-- &-- & & & & \\
&4 & -3 & 0 & -4 & & & & \end{array}$
Quotient = $ 4x^{2}-3x$
Remainder = $f(-2)=-4$
