Divide using synthetic division $$ ( -25x-25 ) \div ( 6x+5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-5&-25&-25\\& & \color{black}{125} \\ \hline &\color{blue}{-25}&\color{orangered}{100} \end{array} $$

The solution is:

$$ \frac{ -25x-25 }{ x+5 } = \color{blue}{-25} ~+~ \frac{ \color{red}{ 100 } }{ x+5 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 5 = 0 $ ( $ x = \color{blue}{ -5 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{-5}&-25&-25\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-5&\color{orangered}{ -25 }&-25\\& & \\ \hline &\color{orangered}{-25}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -5 } \cdot \color{blue}{ \left( -25 \right) } = \color{blue}{ 125 } $.

$$ \begin{array}{c|rr}\color{blue}{-5}&-25&-25\\& & \color{blue}{125} \\ \hline &\color{blue}{-25}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -25 } + \color{orangered}{ 125 } = \color{orangered}{ 100 } $

$$ \begin{array}{c|rr}-5&-25&\color{orangered}{ -25 }\\& & \color{orangered}{125} \\ \hline &\color{blue}{-25}&\color{orangered}{100} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -25 } $ with a remainder of $ \color{red}{ 100 } $.

Synthetic Division Calculator