Divide using synthetic division $$ ( -11x-22 ) \div ( x-4 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}4&-11&-22\\& & \color{black}{-44} \\ \hline &\color{blue}{-11}&\color{orangered}{-66} \end{array} $$

The solution is:

$$ \frac{ -11x-22 }{ x-4 } = \color{blue}{-11} \color{red}{~-~} \frac{ \color{red}{ 66 } }{ x-4 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{4}&-11&-22\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}4&\color{orangered}{ -11 }&-22\\& & \\ \hline &\color{orangered}{-11}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 4 } \cdot \color{blue}{ \left( -11 \right) } = \color{blue}{ -44 } $.

$$ \begin{array}{c|rr}\color{blue}{4}&-11&-22\\& & \color{blue}{-44} \\ \hline &\color{blue}{-11}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -22 } + \color{orangered}{ \left( -44 \right) } = \color{orangered}{ -66 } $

$$ \begin{array}{c|rr}4&-11&\color{orangered}{ -22 }\\& & \color{orangered}{-44} \\ \hline &\color{blue}{-11}&\color{orangered}{-66} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -11 } $ with a remainder of $ \color{red}{ -66 } $.

Synthetic Division Calculator