Answer
$a^2+2a-6$
Work Step by Step
Equating the divisor of the expression to 0 and then solving gives:
\begin{align*}
a-2&=0
\\
a&=2
.\end{align*}
The last row of numbers, $\left\{
1,2,-6,0
\right\},$ gives the coefficient of the quotient and the remainder. Hence, $(
a^3-10a+12
)\div(
a-2
)
$ is equal to
\begin{align*}
a^2+2a-6
.\end{align*}
