Divide using synthetic division $$ ( 75x-40 ) \div ( 2x+1 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-1&75&-40\\& & \color{black}{-75} \\ \hline &\color{blue}{75}&\color{orangered}{-115} \end{array} $$

The solution is:

$$ \frac{ 75x-40 }{ x+1 } = \color{blue}{75} \color{red}{~-~} \frac{ \color{red}{ 115 } }{ x+1 } $$

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

$$ \begin{array}{c|rr}\color{blue}{-1}&75&-40\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-1&\color{orangered}{ 75 }&-40\\& & \\ \hline &\color{orangered}{75}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ 75 } = \color{blue}{ -75 } $.

$$ \begin{array}{c|rr}\color{blue}{-1}&75&-40\\& & \color{blue}{-75} \\ \hline &\color{blue}{75}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -40 } + \color{orangered}{ \left( -75 \right) } = \color{orangered}{ -115 } $

$$ \begin{array}{c|rr}-1&75&\color{orangered}{ -40 }\\& & \color{orangered}{-75} \\ \hline &\color{blue}{75}&\color{orangered}{-115} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 75 } $ with a remainder of $ \color{red}{ -115 } $.

Synthetic Division Calculator