Divide using synthetic division $$ ( 8x+21 ) \div ( 2x+3 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-3&8&21\\& & \color{black}{-24} \\ \hline &\color{blue}{8}&\color{orangered}{-3} \end{array} $$

The solution is:

$$ \frac{ 8x+21 }{ x+3 } = \color{blue}{8} \color{red}{~-~} \frac{ \color{red}{ 3 } }{ x+3 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 3 = 0 $ ( $ x = \color{blue}{ -3 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{-3}&8&21\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-3&\color{orangered}{ 8 }&21\\& & \\ \hline &\color{orangered}{8}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -3 } \cdot \color{blue}{ 8 } = \color{blue}{ -24 } $.

$$ \begin{array}{c|rr}\color{blue}{-3}&8&21\\& & \color{blue}{-24} \\ \hline &\color{blue}{8}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 21 } + \color{orangered}{ \left( -24 \right) } = \color{orangered}{ -3 } $

$$ \begin{array}{c|rr}-3&8&\color{orangered}{ 21 }\\& & \color{orangered}{-24} \\ \hline &\color{blue}{8}&\color{orangered}{-3} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 8 } $ with a remainder of $ \color{red}{ -3 } $.

Synthetic Division Calculator