Check if $ x-3 $ is a factor of $ -4x $.

The synthetic division table is:

$$ \begin{array}{c|rr}3&-4&0\\& & \color{black}{-12} \\ \hline &\color{blue}{-4}&\color{orangered}{-12} \end{array} $$

Because the remainder $ \left( \color{red}{ -12 } \right) $ is not zero, we conclude that the $ x-3 $ is not a factor of $ -4x$.

First we need to create a synthetic division table.

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.

$$ \begin{array}{c|rr}\color{blue}{3}&-4&0\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}3&\color{orangered}{ -4 }&0\\& & \\ \hline &\color{orangered}{-4}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -4 \right) } = \color{blue}{ -12 } $.

$$ \begin{array}{c|rr}\color{blue}{3}&-4&0\\& & \color{blue}{-12} \\ \hline &\color{blue}{-4}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -12 \right) } = \color{orangered}{ -12 } $

$$ \begin{array}{c|rr}3&-4&\color{orangered}{ 0 }\\& & \color{orangered}{-12} \\ \hline &\color{blue}{-4}&\color{orangered}{-12} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -12 }\right)$.

Synthetic Division Calculator