Find remainder when $ -31x-23 $ is divided by $ 0 $.

The synthetic division table is:

$$ \begin{array}{c|rr}0&-31&-23\\& & \color{black}{0} \\ \hline &\color{blue}{-31}&\color{orangered}{-23} \end{array} $$

The remainder when $ -31x-23 $ is divided by $ x $ is $ \, \color{red}{ -23 } $.

We can find remainder using synthetic division method.

Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.

$$ \begin{array}{c|rr}\color{blue}{0}&-31&-23\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}0&\color{orangered}{ -31 }&-23\\& & \\ \hline &\color{orangered}{-31}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -31 \right) } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rr}\color{blue}{0}&-31&-23\\& & \color{blue}{0} \\ \hline &\color{blue}{-31}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -23 } + \color{orangered}{ 0 } = \color{orangered}{ -23 } $

$$ \begin{array}{c|rr}0&-31&\color{orangered}{ -23 }\\& & \color{orangered}{0} \\ \hline &\color{blue}{-31}&\color{orangered}{-23} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -23 }\right) $.

Synthetic Division Calculator