Divide using synthetic division $$ ( 54x+5 ) \div ( x+5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-5&54&5\\& & \color{black}{-270} \\ \hline &\color{blue}{54}&\color{orangered}{-265} \end{array} $$

The solution is:

$$ \frac{ 54x+5 }{ x+5 } = \color{blue}{54} \color{red}{~-~} \frac{ \color{red}{ 265 } }{ x+5 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 5 = 0 $ ( $ x = \color{blue}{ -5 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{-5}&54&5\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-5&\color{orangered}{ 54 }&5\\& & \\ \hline &\color{orangered}{54}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -5 } \cdot \color{blue}{ 54 } = \color{blue}{ -270 } $.

$$ \begin{array}{c|rr}\color{blue}{-5}&54&5\\& & \color{blue}{-270} \\ \hline &\color{blue}{54}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 5 } + \color{orangered}{ \left( -270 \right) } = \color{orangered}{ -265 } $

$$ \begin{array}{c|rr}-5&54&\color{orangered}{ 5 }\\& & \color{orangered}{-270} \\ \hline &\color{blue}{54}&\color{orangered}{-265} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 54 } $ with a remainder of $ \color{red}{ -265 } $.

Synthetic Division Calculator