Answer
$f(3)=-27$
Work Step by Step
The remainder theorem:
If the polynomial f(x) is divided by $x-c$, then the remainder is $f(c).$
Divide $x^{3}-7x^{2}+5x-6$
with $x-3,\qquad (c=3)$
$\begin{array}{rrrrrrrr}
\underline{3}| &1 & -7 & 5 & -6 & & & & \\
& & 3 & -12 & -21 & & & & \\
& --& -- &-- &-- & & & & \\
&1 & -4 & -7 & -27 & & & & \end{array}$
Quotient = $ x^{2}-4x-7$
Remainder = $f(3)=-27$
