Check if $ -6 $ is a factor of $ -3x+5 $.

The synthetic division table is:

$$ \begin{array}{c|rr}0&-3&5\\& & \color{black}{0} \\ \hline &\color{blue}{-3}&\color{orangered}{5} \end{array} $$

Because the remainder $ \left( \color{red}{ 5 } \right) $ is not zero, we conclude that the $ x $ is not a factor of $ -3x+5$.

First we need to create a synthetic division table.

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

$$ \begin{array}{c|rr}\color{blue}{0}&-3&5\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}0&\color{orangered}{ -3 }&5\\& & \\ \hline &\color{orangered}{-3}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -3 \right) } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rr}\color{blue}{0}&-3&5\\& & \color{blue}{0} \\ \hline &\color{blue}{-3}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 5 } + \color{orangered}{ 0 } = \color{orangered}{ 5 } $

$$ \begin{array}{c|rr}0&-3&\color{orangered}{ 5 }\\& & \color{orangered}{0} \\ \hline &\color{blue}{-3}&\color{orangered}{5} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ 5 }\right)$.

Synthetic Division Calculator