Answer
$4m-1$
Work Step by Step
Setup:
Dividing with $m-k$, 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.
$\begin{array}{rrr}
{-5 )} &{4}&{19}&{-5}\\
{ } &{ }&{ } &{ }\\
\hline &{4 }&{ } &{ }\end{array}$
Fill the next entries, column by column:
Middle row: k$\times$(previous bottom row entry)
Bottom row: add the two entries above.
Repeat.
$\begin{array}{rrr}
{-5 )} &{4}&{19}&{-5}\\
{ } &{ }&{-20} &{ 5 }\\
\hline &{4 }&{-1 } &{0 }\end{array}$
Interpret result: Q(x) is the quotient, R(x) the remainder.
$Q(m)=4m-1,\quad R(m)=0$
$\displaystyle \frac{P(m)}{D(m)}=Q(m)+\frac{R(m)}{D(m)}$
$\displaystyle \frac{4m^{2}+19m-5}{m+5}=4m-1$
