Divide using synthetic division $$ ( 7x-20 ) \div ( x+5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-5&7&-20\\& & \color{black}{-35} \\ \hline &\color{blue}{7}&\color{orangered}{-55} \end{array} $$

The solution is:

$$ \frac{ 7x-20 }{ x+5 } = \color{blue}{7} \color{red}{~-~} \frac{ \color{red}{ 55 } }{ x+5 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{-5}&7&-20\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-5&\color{orangered}{ 7 }&-20\\& & \\ \hline &\color{orangered}{7}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -5 } \cdot \color{blue}{ 7 } = \color{blue}{ -35 } $.

$$ \begin{array}{c|rr}\color{blue}{-5}&7&-20\\& & \color{blue}{-35} \\ \hline &\color{blue}{7}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -20 } + \color{orangered}{ \left( -35 \right) } = \color{orangered}{ -55 } $

$$ \begin{array}{c|rr}-5&7&\color{orangered}{ -20 }\\& & \color{orangered}{-35} \\ \hline &\color{blue}{7}&\color{orangered}{-55} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 7 } $ with a remainder of $ \color{red}{ -55 } $.

Synthetic Division Calculator