Answer
$4y+11+\dfrac{24}{y-4}$
Work Step by Step
Setup: (the variable is $y$ 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.
$\begin{array}{rrr}
{4)} &{4}&{-5}&{-20}\\
{ } &{ }&{ } &{ }\\
\hline &{4 }&{ } &{ }\end{array}$
Fill the next entries, column by column:
Middle row: k$\times$(previous bottom row entry)
Bottom row: add the two entries above.
Repeat.
$\begin{array}{rrr}
{4)} &{4}&{-5}&{-20}\\
{ } &{ }&{16 } &{44 }\\
\hline &{4 }&{11 } &{24 }\end{array}$
Interpret result:
Q(x) is the quotient, R(x) the remainder. $\displaystyle \frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$
$Q(y)=4y+11,\quad R(y)=24$
$\displaystyle \frac{4y^{2}-5y-20}{y-4}=4y+11+\frac{24}{y-4}$
