Divide using synthetic division $$ ( -x-10 ) \div ( 2x-1 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}1&-1&-10\\& & \color{black}{-1} \\ \hline &\color{blue}{-1}&\color{orangered}{-11} \end{array} $$

The solution is:

$$ \frac{ -x-10 }{ x-1 } = \color{blue}{-1} \color{red}{~-~} \frac{ \color{red}{ 11 } }{ x-1 } $$

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.

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

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

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

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

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

Step 3 : Add down last column: $ \color{orangered}{ -10 } + \color{orangered}{ \left( -1 \right) } = \color{orangered}{ -11 } $

$$ \begin{array}{c|rr}1&-1&\color{orangered}{ -10 }\\& & \color{orangered}{-1} \\ \hline &\color{blue}{-1}&\color{orangered}{-11} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -1 } $ with a remainder of $ \color{red}{ -11 } $.

Synthetic Division Calculator