Divide using synthetic division $$ ( -13x-12 ) \div ( x-4 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}4&-13&-12\\& & \color{black}{-52} \\ \hline &\color{blue}{-13}&\color{orangered}{-64} \end{array} $$

The solution is:

$$ \frac{ -13x-12 }{ x-4 } = \color{blue}{-13} \color{red}{~-~} \frac{ \color{red}{ 64 } }{ x-4 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -4 = 0 $ ( $ x = \color{blue}{ 4 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{4}&-13&-12\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}4&\color{orangered}{ -13 }&-12\\& & \\ \hline &\color{orangered}{-13}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 4 } \cdot \color{blue}{ \left( -13 \right) } = \color{blue}{ -52 } $.

$$ \begin{array}{c|rr}\color{blue}{4}&-13&-12\\& & \color{blue}{-52} \\ \hline &\color{blue}{-13}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -12 } + \color{orangered}{ \left( -52 \right) } = \color{orangered}{ -64 } $

$$ \begin{array}{c|rr}4&-13&\color{orangered}{ -12 }\\& & \color{orangered}{-52} \\ \hline &\color{blue}{-13}&\color{orangered}{-64} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -13 } $ with a remainder of $ \color{red}{ -64 } $.

Synthetic Division Calculator