Divide using synthetic division $$ ( 26x+38 ) \div ( 3x-1 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}1&26&38\\& & \color{black}{26} \\ \hline &\color{blue}{26}&\color{orangered}{64} \end{array} $$

The solution is:

$$ \frac{ 26x+38 }{ x-1 } = \color{blue}{26} ~+~ \frac{ \color{red}{ 64 } }{ x-1 } $$

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

$$ \begin{array}{c|rr}\color{blue}{1}&26&38\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}1&\color{orangered}{ 26 }&38\\& & \\ \hline &\color{orangered}{26}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ 26 } = \color{blue}{ 26 } $.

$$ \begin{array}{c|rr}\color{blue}{1}&26&38\\& & \color{blue}{26} \\ \hline &\color{blue}{26}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 38 } + \color{orangered}{ 26 } = \color{orangered}{ 64 } $

$$ \begin{array}{c|rr}1&26&\color{orangered}{ 38 }\\& & \color{orangered}{26} \\ \hline &\color{blue}{26}&\color{orangered}{64} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 26 } $ with a remainder of $ \color{red}{ 64 } $.

Synthetic Division Calculator