Check if $ x-12 $ is a factor of $ 3x+2 $.

The synthetic division table is:

$$ \begin{array}{c|rr}12&3&2\\& & \color{black}{36} \\ \hline &\color{blue}{3}&\color{orangered}{38} \end{array} $$

Because the remainder $ \left( \color{red}{ 38 } \right) $ is not zero, we conclude that the $ x-12 $ 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 -12 = 0 $ ( $ x = \color{blue}{ 12 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{12}&3&2\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}12&\color{orangered}{ 3 }&2\\& & \\ \hline &\color{orangered}{3}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 12 } \cdot \color{blue}{ 3 } = \color{blue}{ 36 } $.

$$ \begin{array}{c|rr}\color{blue}{12}&3&2\\& & \color{blue}{36} \\ \hline &\color{blue}{3}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 2 } + \color{orangered}{ 36 } = \color{orangered}{ 38 } $

$$ \begin{array}{c|rr}12&3&\color{orangered}{ 2 }\\& & \color{orangered}{36} \\ \hline &\color{blue}{3}&\color{orangered}{38} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ 38 }\right)$.

Synthetic Division Calculator