Divide using synthetic division $$ ( 7x ) \div ( x-13 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}13&7&0\\& & \color{black}{91} \\ \hline &\color{blue}{7}&\color{orangered}{91} \end{array} $$

The solution is:

$$ \frac{ 7x }{ x-13 } = \color{blue}{7} ~+~ \frac{ \color{red}{ 91 } }{ x-13 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -13 = 0 $ ( $ x = \color{blue}{ 13 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{13}&7&0\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}13&\color{orangered}{ 7 }&0\\& & \\ \hline &\color{orangered}{7}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 13 } \cdot \color{blue}{ 7 } = \color{blue}{ 91 } $.

$$ \begin{array}{c|rr}\color{blue}{13}&7&0\\& & \color{blue}{91} \\ \hline &\color{blue}{7}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 91 } = \color{orangered}{ 91 } $

$$ \begin{array}{c|rr}13&7&\color{orangered}{ 0 }\\& & \color{orangered}{91} \\ \hline &\color{blue}{7}&\color{orangered}{91} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 7 } $ with a remainder of $ \color{red}{ 91 } $.

Synthetic Division Calculator