Divide using synthetic division $$ ( -17x+36 ) \div ( x-2 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}2&-17&36\\& & \color{black}{-34} \\ \hline &\color{blue}{-17}&\color{orangered}{2} \end{array} $$

The solution is:

$$ \frac{ -17x+36 }{ x-2 } = \color{blue}{-17} ~+~ \frac{ \color{red}{ 2 } }{ x-2 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -2 = 0 $ ( $ x = \color{blue}{ 2 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{2}&-17&36\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}2&\color{orangered}{ -17 }&36\\& & \\ \hline &\color{orangered}{-17}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 2 } \cdot \color{blue}{ \left( -17 \right) } = \color{blue}{ -34 } $.

$$ \begin{array}{c|rr}\color{blue}{2}&-17&36\\& & \color{blue}{-34} \\ \hline &\color{blue}{-17}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 36 } + \color{orangered}{ \left( -34 \right) } = \color{orangered}{ 2 } $

$$ \begin{array}{c|rr}2&-17&\color{orangered}{ 36 }\\& & \color{orangered}{-34} \\ \hline &\color{blue}{-17}&\color{orangered}{2} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -17 } $ with a remainder of $ \color{red}{ 2 } $.

Synthetic Division Calculator