Divide using synthetic division $$ ( 11x+25 ) \div ( x+5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}-5&11&25\\& & \color{black}{-55} \\ \hline &\color{blue}{11}&\color{orangered}{-30} \end{array} $$

The solution is:

$$ \frac{ 11x+25 }{ x+5 } = \color{blue}{11} \color{red}{~-~} \frac{ \color{red}{ 30 } }{ x+5 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{-5}&11&25\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-5&\color{orangered}{ 11 }&25\\& & \\ \hline &\color{orangered}{11}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -5 } \cdot \color{blue}{ 11 } = \color{blue}{ -55 } $.

$$ \begin{array}{c|rr}\color{blue}{-5}&11&25\\& & \color{blue}{-55} \\ \hline &\color{blue}{11}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 25 } + \color{orangered}{ \left( -55 \right) } = \color{orangered}{ -30 } $

$$ \begin{array}{c|rr}-5&11&\color{orangered}{ 25 }\\& & \color{orangered}{-55} \\ \hline &\color{blue}{11}&\color{orangered}{-30} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 11 } $ with a remainder of $ \color{red}{ -30 } $.

Synthetic Division Calculator