Answer
$x^2-x+2$
Work Step by Step
Equating the divisor of the given expression, $
(x^3-4x^2+5x-6)\div(x-3)
,$ to zero and solving for the variable results in
\begin{align*}
x-3&=0
\\
x&=3
.\end{align*}
The last row of numbers, $\left\{
1,-1,2,0
\right\},$ gives the coefficient of the quotient and the remainder. Hence, $(x^3-4x^2+5x-6)\div(x-3)$ is equal to
\begin{align*}
x^2-x+2
.\end{align*}
