Divide using synthetic division $$ ( 30x-86 ) \div ( x-9 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}9&30&-86\\& & \color{black}{270} \\ \hline &\color{blue}{30}&\color{orangered}{184} \end{array} $$

The solution is:

$$ \frac{ 30x-86 }{ x-9 } = \color{blue}{30} ~+~ \frac{ \color{red}{ 184 } }{ x-9 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -9 = 0 $ ( $ x = \color{blue}{ 9 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{9}&30&-86\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}9&\color{orangered}{ 30 }&-86\\& & \\ \hline &\color{orangered}{30}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 9 } \cdot \color{blue}{ 30 } = \color{blue}{ 270 } $.

$$ \begin{array}{c|rr}\color{blue}{9}&30&-86\\& & \color{blue}{270} \\ \hline &\color{blue}{30}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -86 } + \color{orangered}{ 270 } = \color{orangered}{ 184 } $

$$ \begin{array}{c|rr}9&30&\color{orangered}{ -86 }\\& & \color{orangered}{270} \\ \hline &\color{blue}{30}&\color{orangered}{184} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 30 } $ with a remainder of $ \color{red}{ 184 } $.

Synthetic Division Calculator