Divide using synthetic division $$ ( -9x+21 ) \div ( x-5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}5&-9&21\\& & \color{black}{-45} \\ \hline &\color{blue}{-9}&\color{orangered}{-24} \end{array} $$

The solution is:

$$ \frac{ -9x+21 }{ x-5 } = \color{blue}{-9} \color{red}{~-~} \frac{ \color{red}{ 24 } }{ x-5 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -5 = 0 $ ( $ x = \color{blue}{ 5 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{5}&-9&21\\& & \\ \hline && \end{array} $$

Step 1 : Bring down the leading coefficient to the bottom row.

$$ \begin{array}{c|rr}5&\color{orangered}{ -9 }&21\\& & \\ \hline &\color{orangered}{-9}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 5 } \cdot \color{blue}{ \left( -9 \right) } = \color{blue}{ -45 } $.

$$ \begin{array}{c|rr}\color{blue}{5}&-9&21\\& & \color{blue}{-45} \\ \hline &\color{blue}{-9}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 21 } + \color{orangered}{ \left( -45 \right) } = \color{orangered}{ -24 } $

$$ \begin{array}{c|rr}5&-9&\color{orangered}{ 21 }\\& & \color{orangered}{-45} \\ \hline &\color{blue}{-9}&\color{orangered}{-24} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -9 } $ with a remainder of $ \color{red}{ -24 } $.

Synthetic Division Calculator