Answer
$f(4)=-25$
Work Step by Step
The remainder theorem:
If the polynomial f(x) is divided by $x-c$, then the remainder is $f(c).$
Divide $2x^{3}-11x^{2}+7x-5$
with $x-4,\qquad (c=4)$
$\begin{array}{rrrrrrrr}
\underline{4}| &2 & -11 & 7 & -5 & & & & \\
& & 8 & -12 & -20 & & & & \\
& --& -- &-- &-- & & & & \\
&2 & -3 & -5 & -25 & & & & \end{array}$
Quotient = $ 2x^{2}-3x-5$
Remainder = $f(4)=-25$
