Find remainder when $ -x+87 $ is divided by $ 2x+5 $.

The synthetic division table is:

$$ \begin{array}{c|rr}-5&-1&87\\& & \color{black}{5} \\ \hline &\color{blue}{-1}&\color{orangered}{92} \end{array} $$

The remainder when $ -x+87 $ is divided by $ x+5 $ is $ \, \color{red}{ 92 } $.

We can find remainder using synthetic division method.

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 5 = 0 $ ( $ x = \color{blue}{ -5 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{-5}&-1&87\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-5&\color{orangered}{ -1 }&87\\& & \\ \hline &\color{orangered}{-1}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -5 } \cdot \color{blue}{ \left( -1 \right) } = \color{blue}{ 5 } $.

$$ \begin{array}{c|rr}\color{blue}{-5}&-1&87\\& & \color{blue}{5} \\ \hline &\color{blue}{-1}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 87 } + \color{orangered}{ 5 } = \color{orangered}{ 92 } $

$$ \begin{array}{c|rr}-5&-1&\color{orangered}{ 87 }\\& & \color{orangered}{5} \\ \hline &\color{blue}{-1}&\color{orangered}{92} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ 92 }\right) $.

Synthetic Division Calculator