Divide using synthetic division $$ ( 2x+3 ) \div ( 4x ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}0&2&3\\& & \color{black}{0} \\ \hline &\color{blue}{2}&\color{orangered}{3} \end{array} $$

The solution is:

$$ \frac{ 2x+3 }{ x } = \color{blue}{2} ~+~ \frac{ \color{red}{ 3 } }{ x } $$

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

$$ \begin{array}{c|rr}\color{blue}{0}&2&3\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}0&\color{orangered}{ 2 }&3\\& & \\ \hline &\color{orangered}{2}& \end{array} $$

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

$$ \begin{array}{c|rr}\color{blue}{0}&2&3\\& & \color{blue}{0} \\ \hline &\color{blue}{2}& \end{array} $$

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

$$ \begin{array}{c|rr}0&2&\color{orangered}{ 3 }\\& & \color{orangered}{0} \\ \hline &\color{blue}{2}&\color{orangered}{3} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 2 } $ with a remainder of $ \color{red}{ 3 } $.

Synthetic Division Calculator