Find remainder when $ x-3 $ is divided by $ -3 $.

The synthetic division table is:

$$ \begin{array}{c|rr}0&1&-3\\& & \color{black}{0} \\ \hline &\color{blue}{1}&\color{orangered}{-3} \end{array} $$

The remainder when $ x-3 $ is divided by $ x $ is $ \, \color{red}{ -3 } $.

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.

$$ \begin{array}{c|rr}\color{blue}{0}&1&-3\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}0&\color{orangered}{ 1 }&-3\\& & \\ \hline &\color{orangered}{1}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 1 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rr}\color{blue}{0}&1&-3\\& & \color{blue}{0} \\ \hline &\color{blue}{1}& \end{array} $$

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

$$ \begin{array}{c|rr}0&1&\color{orangered}{ -3 }\\& & \color{orangered}{0} \\ \hline &\color{blue}{1}&\color{orangered}{-3} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -3 }\right) $.

Synthetic Division Calculator