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

The synthetic division table is:

$$ \begin{array}{c|rr}-3&3&2\\& & \color{black}{-9} \\ \hline &\color{blue}{3}&\color{orangered}{-7} \end{array} $$

Because the remainder $ \left( \color{red}{ -7 } \right) $ is not zero, we conclude that the $ x+3 $ 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 from $ x + 3 = 0 $ ( $ x = \color{blue}{ -3 } $ ) at the left.

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

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

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

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

$$ \begin{array}{c|rr}\color{blue}{-3}&3&2\\& & \color{blue}{-9} \\ \hline &\color{blue}{3}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 2 } + \color{orangered}{ \left( -9 \right) } = \color{orangered}{ -7 } $

$$ \begin{array}{c|rr}-3&3&\color{orangered}{ 2 }\\& & \color{orangered}{-9} \\ \hline &\color{blue}{3}&\color{orangered}{-7} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -7 }\right)$.

Synthetic Division Calculator