Divide using synthetic division $$ ( 8x-2 ) \div ( 4x-1 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}1&8&-2\\& & \color{black}{8} \\ \hline &\color{blue}{8}&\color{orangered}{6} \end{array} $$

The solution is:

$$ \frac{ 8x-2 }{ x-1 } = \color{blue}{8} ~+~ \frac{ \color{red}{ 6 } }{ x-1 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{1}&8&-2\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}1&\color{orangered}{ 8 }&-2\\& & \\ \hline &\color{orangered}{8}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ 8 } = \color{blue}{ 8 } $.

$$ \begin{array}{c|rr}\color{blue}{1}&8&-2\\& & \color{blue}{8} \\ \hline &\color{blue}{8}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -2 } + \color{orangered}{ 8 } = \color{orangered}{ 6 } $

$$ \begin{array}{c|rr}1&8&\color{orangered}{ -2 }\\& & \color{orangered}{8} \\ \hline &\color{blue}{8}&\color{orangered}{6} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 8 } $ with a remainder of $ \color{red}{ 6 } $.

Synthetic Division Calculator