Check if $ x $ is a factor of $ 3x+2 $.

The synthetic division table is:

$$ \begin{array}{c|rr}0&3&2\\& & \color{black}{0} \\ \hline &\color{blue}{3}&\color{orangered}{2} \end{array} $$

Because the remainder $ \left( \color{red}{ 2 } \right) $ is not zero, we conclude that the $ x $ is not a factor of $ 3x+2$.

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.

$$ \begin{array}{c|rr}\color{blue}{0}&3&2\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}0&\color{orangered}{ 3 }&2\\& & \\ \hline &\color{orangered}{3}& \end{array} $$

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

$$ \begin{array}{c|rr}\color{blue}{0}&3&2\\& & \color{blue}{0} \\ \hline &\color{blue}{3}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 2 } + \color{orangered}{ 0 } = \color{orangered}{ 2 } $

$$ \begin{array}{c|rr}0&3&\color{orangered}{ 2 }\\& & \color{orangered}{0} \\ \hline &\color{blue}{3}&\color{orangered}{2} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ 2 }\right)$.

Synthetic Division Calculator