Answer
$a^2+3a-5$
Work Step by Step
Equating the divisor of the expression to 0 and then solving gives:
\begin{align*}
a-3&=0
\\
a&=3
.\end{align*}
The last row of numbers, $\left\{
1,3,-5,0
\right\},$ gives the coefficient of the quotient and the remainder. Hence, $(
a^3-14a+15
)\div(
a-3
)
$ is equal to
\begin{align*}
a^2+3a-5
.\end{align*}