Answer
$5p^{2}-11p+14$
Work Step by Step
Setup: (the variable is $p$ instead of $x$).
Dividing with $x-k$, place k as the top left entry.
List coefficients of the numerator (0 for missing powers) in the first row.
Copy the leading coefficient to the bottom row, same column.
$\begin{array}{rrr}
{-1\ \ )} &{5}&{-6}&{3}&{14}&{ }\\
{ } &{ }&{ }&{ }&{ } &{ }\\
\hline &{5 }&{ }&{ }&{ } &{ }\end{array}$
Fill the next entries, column by column:
Middle row: k$\times$(previous bottom row entry)
Bottom row: add the two entries above.
Repeat.
$\begin{array}{rrr}
{-1\ \ )} &{5}&{-6}&{3}&{14}&{ }\\
{ } &{ }&{-5}&{ 11}&{ -14} &{ }\\
\hline &{5 }&{ -11}&{14 }&{ 0} &{ }\end{array}$
Interpret result:
Q(x) is the quotient, R(x) the remainder. $\displaystyle \frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$
$Q(p)=5p^{2}-11p+14\quad R(p)=0$
$\displaystyle \frac{5p^{3}-6p^{2}+3p+14}{p+1}= 5p^{2}-11p+14$
