Divide using synthetic division $$ ( -x+8 ) \div ( x+2 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-2&-1&8\\& & \color{black}{2} \\ \hline &\color{blue}{-1}&\color{orangered}{10} \end{array} $$

The solution is:

$$ \frac{ -x+8 }{ x+2 } = \color{blue}{-1} ~+~ \frac{ \color{red}{ 10 } }{ x+2 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{-2}&-1&8\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-2&\color{orangered}{ -1 }&8\\& & \\ \hline &\color{orangered}{-1}& \end{array} $$

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

$$ \begin{array}{c|rr}\color{blue}{-2}&-1&8\\& & \color{blue}{2} \\ \hline &\color{blue}{-1}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 8 } + \color{orangered}{ 2 } = \color{orangered}{ 10 } $

$$ \begin{array}{c|rr}-2&-1&\color{orangered}{ 8 }\\& & \color{orangered}{2} \\ \hline &\color{blue}{-1}&\color{orangered}{10} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -1 } $ with a remainder of $ \color{red}{ 10 } $.

Synthetic Division Calculator