Divide using synthetic division $$ ( -15x+7 ) \div ( x+5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-5&-15&7\\& & \color{black}{75} \\ \hline &\color{blue}{-15}&\color{orangered}{82} \end{array} $$

The solution is:

$$ \frac{ -15x+7 }{ x+5 } = \color{blue}{-15} ~+~ \frac{ \color{red}{ 82 } }{ x+5 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{-5}&-15&7\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-5&\color{orangered}{ -15 }&7\\& & \\ \hline &\color{orangered}{-15}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -5 } \cdot \color{blue}{ \left( -15 \right) } = \color{blue}{ 75 } $.

$$ \begin{array}{c|rr}\color{blue}{-5}&-15&7\\& & \color{blue}{75} \\ \hline &\color{blue}{-15}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 7 } + \color{orangered}{ 75 } = \color{orangered}{ 82 } $

$$ \begin{array}{c|rr}-5&-15&\color{orangered}{ 7 }\\& & \color{orangered}{75} \\ \hline &\color{blue}{-15}&\color{orangered}{82} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -15 } $ with a remainder of $ \color{red}{ 82 } $.

Synthetic Division Calculator