Divide using synthetic division $$ ( -6x+7 ) \div ( x+1 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-1&-6&7\\& & \color{black}{6} \\ \hline &\color{blue}{-6}&\color{orangered}{13} \end{array} $$

The solution is:

$$ \frac{ -6x+7 }{ x+1 } = \color{blue}{-6} ~+~ \frac{ \color{red}{ 13 } }{ x+1 } $$

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

$$ \begin{array}{c|rr}\color{blue}{-1}&-6&7\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-1&\color{orangered}{ -6 }&7\\& & \\ \hline &\color{orangered}{-6}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ \left( -6 \right) } = \color{blue}{ 6 } $.

$$ \begin{array}{c|rr}\color{blue}{-1}&-6&7\\& & \color{blue}{6} \\ \hline &\color{blue}{-6}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 7 } + \color{orangered}{ 6 } = \color{orangered}{ 13 } $

$$ \begin{array}{c|rr}-1&-6&\color{orangered}{ 7 }\\& & \color{orangered}{6} \\ \hline &\color{blue}{-6}&\color{orangered}{13} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -6 } $ with a remainder of $ \color{red}{ 13 } $.

Synthetic Division Calculator