Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 1 = 0 $ ( $ x = \color{blue}{ -1 } $ ) at the left.

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

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

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

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ \left( -2 \right) } = \color{blue}{ 2 } $.

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

Step 3 : Add down last column: $ \color{orangered}{ 2 } + \color{orangered}{ 2 } = \color{orangered}{ 4 } $

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

Bottom line represents the quotient $ \color{blue}{ -2 } $ with a remainder of $ \color{red}{ 4 } $.

Synthetic Division Calculator