Divide using synthetic division $$ ( -13x+8 ) \div ( x+3 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-3&-13&8\\& & \color{black}{39} \\ \hline &\color{blue}{-13}&\color{orangered}{47} \end{array} $$

The solution is:

$$ \frac{ -13x+8 }{ x+3 } = \color{blue}{-13} ~+~ \frac{ \color{red}{ 47 } }{ x+3 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{-3}&-13&8\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-3&\color{orangered}{ -13 }&8\\& & \\ \hline &\color{orangered}{-13}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -3 } \cdot \color{blue}{ \left( -13 \right) } = \color{blue}{ 39 } $.

$$ \begin{array}{c|rr}\color{blue}{-3}&-13&8\\& & \color{blue}{39} \\ \hline &\color{blue}{-13}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 8 } + \color{orangered}{ 39 } = \color{orangered}{ 47 } $

$$ \begin{array}{c|rr}-3&-13&\color{orangered}{ 8 }\\& & \color{orangered}{39} \\ \hline &\color{blue}{-13}&\color{orangered}{47} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -13 } $ with a remainder of $ \color{red}{ 47 } $.

Synthetic Division Calculator