Answer
$3x^2+2x-1+\dfrac{11}{x-4}$
Work Step by Step
Equating the divisor of the expression to 0 and then solving gives:
\begin{align*}
x-4&=0
\\
x&=4
.\end{align*}
The last row of numbers, $\left\{
3,2,-1,11
\right\},$ gives the coefficient of the quotient and the remainder. Hence, $(
3x^3-10x^2-9x+15
)\div(
x-4
)
$ is equal to
\begin{align*}
3x^2+2x-1+\dfrac{11}{x-4}
.\end{align*}
