Divide using synthetic division $$ ( 5x-1 ) \div ( 1 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}0&5&-1\\& & \color{black}{0} \\ \hline &\color{blue}{5}&\color{orangered}{-1} \end{array} $$

The solution is:

$$ \frac{ 5x-1 }{ x } = \color{blue}{5} \color{red}{~-~} \frac{ \color{red}{ 1 } }{ x } $$

Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.

$$ \begin{array}{c|rr}\color{blue}{0}&5&-1\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}0&\color{orangered}{ 5 }&-1\\& & \\ \hline &\color{orangered}{5}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 5 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rr}\color{blue}{0}&5&-1\\& & \color{blue}{0} \\ \hline &\color{blue}{5}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -1 } + \color{orangered}{ 0 } = \color{orangered}{ -1 } $

$$ \begin{array}{c|rr}0&5&\color{orangered}{ -1 }\\& & \color{orangered}{0} \\ \hline &\color{blue}{5}&\color{orangered}{-1} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 5 } $ with a remainder of $ \color{red}{ -1 } $.

Synthetic Division Calculator