Divide using synthetic division $$ ( -12x+12 ) \div ( x-2 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}2&-12&12\\& & \color{black}{-24} \\ \hline &\color{blue}{-12}&\color{orangered}{-12} \end{array} $$

The solution is:

$$ \frac{ -12x+12 }{ x-2 } = \color{blue}{-12} \color{red}{~-~} \frac{ \color{red}{ 12 } }{ x-2 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -2 = 0 $ ( $ x = \color{blue}{ 2 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{2}&-12&12\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}2&\color{orangered}{ -12 }&12\\& & \\ \hline &\color{orangered}{-12}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 2 } \cdot \color{blue}{ \left( -12 \right) } = \color{blue}{ -24 } $.

$$ \begin{array}{c|rr}\color{blue}{2}&-12&12\\& & \color{blue}{-24} \\ \hline &\color{blue}{-12}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 12 } + \color{orangered}{ \left( -24 \right) } = \color{orangered}{ -12 } $

$$ \begin{array}{c|rr}2&-12&\color{orangered}{ 12 }\\& & \color{orangered}{-24} \\ \hline &\color{blue}{-12}&\color{orangered}{-12} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -12 } $ with a remainder of $ \color{red}{ -12 } $.

Synthetic Division Calculator