Divide using synthetic division $$ ( -x+250 ) \div ( -x+40 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-40&-1&250\\& & \color{black}{40} \\ \hline &\color{blue}{-1}&\color{orangered}{290} \end{array} $$

The solution is:

$$ \frac{ -x+250 }{ x+40 } = \color{blue}{-1} ~+~ \frac{ \color{red}{ 290 } }{ x+40 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 40 = 0 $ ( $ x = \color{blue}{ -40 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{-40}&-1&250\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-40&\color{orangered}{ -1 }&250\\& & \\ \hline &\color{orangered}{-1}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -40 } \cdot \color{blue}{ \left( -1 \right) } = \color{blue}{ 40 } $.

$$ \begin{array}{c|rr}\color{blue}{-40}&-1&250\\& & \color{blue}{40} \\ \hline &\color{blue}{-1}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 250 } + \color{orangered}{ 40 } = \color{orangered}{ 290 } $

$$ \begin{array}{c|rr}-40&-1&\color{orangered}{ 250 }\\& & \color{orangered}{40} \\ \hline &\color{blue}{-1}&\color{orangered}{290} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -1 } $ with a remainder of $ \color{red}{ 290 } $.

Synthetic Division Calculator