Divide using synthetic division $$ ( 3x-5 ) \div ( x-5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}5&3&-5\\& & \color{black}{15} \\ \hline &\color{blue}{3}&\color{orangered}{10} \end{array} $$

The solution is:

$$ \frac{ 3x-5 }{ x-5 } = \color{blue}{3} ~+~ \frac{ \color{red}{ 10 } }{ x-5 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{5}&3&-5\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}5&\color{orangered}{ 3 }&-5\\& & \\ \hline &\color{orangered}{3}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 5 } \cdot \color{blue}{ 3 } = \color{blue}{ 15 } $.

$$ \begin{array}{c|rr}\color{blue}{5}&3&-5\\& & \color{blue}{15} \\ \hline &\color{blue}{3}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -5 } + \color{orangered}{ 15 } = \color{orangered}{ 10 } $

$$ \begin{array}{c|rr}5&3&\color{orangered}{ -5 }\\& & \color{orangered}{15} \\ \hline &\color{blue}{3}&\color{orangered}{10} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 3 } $ with a remainder of $ \color{red}{ 10 } $.

Synthetic Division Calculator