The synthetic division table is:
$$ \begin{array}{c|rr}-4&30&-3\\& & \color{black}{-120} \\ \hline &\color{blue}{30}&\color{orangered}{-123} \end{array} $$The solution is:
$$ \frac{ 30x-3 }{ x+4 } = \color{blue}{30} \color{red}{~-~} \frac{ \color{red}{ 123 } }{ x+4 } $$Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 4 = 0 $ ( $ x = \color{blue}{ -4 } $ ) at the left.
$$ \begin{array}{c|rr}\color{blue}{-4}&30&-3\\& & \\ \hline && \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rr}-4&\color{orangered}{ 30 }&-3\\& & \\ \hline &\color{orangered}{30}& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ 30 } = \color{blue}{ -120 } $.
$$ \begin{array}{c|rr}\color{blue}{-4}&30&-3\\& & \color{blue}{-120} \\ \hline &\color{blue}{30}& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ -3 } + \color{orangered}{ \left( -120 \right) } = \color{orangered}{ -123 } $
$$ \begin{array}{c|rr}-4&30&\color{orangered}{ -3 }\\& & \color{orangered}{-120} \\ \hline &\color{blue}{30}&\color{orangered}{-123} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 30 } $ with a remainder of $ \color{red}{ -123 } $.