Divide using synthetic division $$ ( -28x-5 ) \div ( x-3 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}3&-28&-5\\& & \color{black}{-84} \\ \hline &\color{blue}{-28}&\color{orangered}{-89} \end{array} $$

The solution is:

$$ \frac{ -28x-5 }{ x-3 } = \color{blue}{-28} \color{red}{~-~} \frac{ \color{red}{ 89 } }{ x-3 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -3 = 0 $ ( $ x = \color{blue}{ 3 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{3}&-28&-5\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}3&\color{orangered}{ -28 }&-5\\& & \\ \hline &\color{orangered}{-28}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -28 \right) } = \color{blue}{ -84 } $.

$$ \begin{array}{c|rr}\color{blue}{3}&-28&-5\\& & \color{blue}{-84} \\ \hline &\color{blue}{-28}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -5 } + \color{orangered}{ \left( -84 \right) } = \color{orangered}{ -89 } $

$$ \begin{array}{c|rr}3&-28&\color{orangered}{ -5 }\\& & \color{orangered}{-84} \\ \hline &\color{blue}{-28}&\color{orangered}{-89} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -28 } $ with a remainder of $ \color{red}{ -89 } $.

Synthetic Division Calculator