Check if $ x+2 $ is a factor of $ 2x+1 $.

The synthetic division table is:

$$ \begin{array}{c|rr}-2&2&1\\& & \color{black}{-4} \\ \hline &\color{blue}{2}&\color{orangered}{-3} \end{array} $$

Because the remainder $ \left( \color{red}{ -3 } \right) $ is not zero, we conclude that the $ x+2 $ is not a factor of $ 2x+1$.

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 + 2 = 0 $ ( $ x = \color{blue}{ -2 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{-2}&2&1\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-2&\color{orangered}{ 2 }&1\\& & \\ \hline &\color{orangered}{2}& \end{array} $$

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

$$ \begin{array}{c|rr}\color{blue}{-2}&2&1\\& & \color{blue}{-4} \\ \hline &\color{blue}{2}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 1 } + \color{orangered}{ \left( -4 \right) } = \color{orangered}{ -3 } $

$$ \begin{array}{c|rr}-2&2&\color{orangered}{ 1 }\\& & \color{orangered}{-4} \\ \hline &\color{blue}{2}&\color{orangered}{-3} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -3 }\right)$.

Synthetic Division Calculator