Divide using synthetic division $$ ( 4x-13 ) \div ( 3x+2 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-2&4&-13\\& & \color{black}{-8} \\ \hline &\color{blue}{4}&\color{orangered}{-21} \end{array} $$

The solution is:

$$ \frac{ 4x-13 }{ x+2 } = \color{blue}{4} \color{red}{~-~} \frac{ \color{red}{ 21 } }{ x+2 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{-2}&4&-13\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-2&\color{orangered}{ 4 }&-13\\& & \\ \hline &\color{orangered}{4}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -2 } \cdot \color{blue}{ 4 } = \color{blue}{ -8 } $.

$$ \begin{array}{c|rr}\color{blue}{-2}&4&-13\\& & \color{blue}{-8} \\ \hline &\color{blue}{4}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -13 } + \color{orangered}{ \left( -8 \right) } = \color{orangered}{ -21 } $

$$ \begin{array}{c|rr}-2&4&\color{orangered}{ -13 }\\& & \color{orangered}{-8} \\ \hline &\color{blue}{4}&\color{orangered}{-21} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 4 } $ with a remainder of $ \color{red}{ -21 } $.

Synthetic Division Calculator