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

The synthetic division table is:

$$ \begin{array}{c|rr}3&-3&0\\& & \color{black}{-9} \\ \hline &\color{blue}{-3}&\color{orangered}{-9} \end{array} $$

The remainder when $ -3x $ is divided by $ x-3 $ is $ \, \color{red}{ -9 } $.

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 -3 = 0 $ ( $ x = \color{blue}{ 3 } $ ) at the left.

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

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

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

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -3 \right) } = \color{blue}{ -9 } $.

$$ \begin{array}{c|rr}\color{blue}{3}&-3&0\\& & \color{blue}{-9} \\ \hline &\color{blue}{-3}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -9 \right) } = \color{orangered}{ -9 } $

$$ \begin{array}{c|rr}3&-3&\color{orangered}{ 0 }\\& & \color{orangered}{-9} \\ \hline &\color{blue}{-3}&\color{orangered}{-9} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -9 }\right) $.

Synthetic Division Calculator