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

The synthetic division table is:

$$ \begin{array}{c|rr}-3&1&-4\\& & \color{black}{-3} \\ \hline &\color{blue}{1}&\color{orangered}{-7} \end{array} $$

The solution is:

$$ \frac{ x-4 }{ x+3 } = \color{blue}{1} \color{red}{~-~} \frac{ \color{red}{ 7 } }{ x+3 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{-3}&1&-4\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-3&\color{orangered}{ 1 }&-4\\& & \\ \hline &\color{orangered}{1}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -3 } \cdot \color{blue}{ 1 } = \color{blue}{ -3 } $.

$$ \begin{array}{c|rr}\color{blue}{-3}&1&-4\\& & \color{blue}{-3} \\ \hline &\color{blue}{1}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -4 } + \color{orangered}{ \left( -3 \right) } = \color{orangered}{ -7 } $

$$ \begin{array}{c|rr}-3&1&\color{orangered}{ -4 }\\& & \color{orangered}{-3} \\ \hline &\color{blue}{1}&\color{orangered}{-7} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 1 } $ with a remainder of $ \color{red}{ -7 } $.

Synthetic Division Calculator