Divide using synthetic division $$ ( -13x+16 ) \div ( 2x-5 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}5&-13&16\\& & \color{black}{-65} \\ \hline &\color{blue}{-13}&\color{orangered}{-49} \end{array} $$

The solution is:

$$ \frac{ -13x+16 }{ x-5 } = \color{blue}{-13} \color{red}{~-~} \frac{ \color{red}{ 49 } }{ x-5 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{5}&-13&16\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}5&\color{orangered}{ -13 }&16\\& & \\ \hline &\color{orangered}{-13}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 5 } \cdot \color{blue}{ \left( -13 \right) } = \color{blue}{ -65 } $.

$$ \begin{array}{c|rr}\color{blue}{5}&-13&16\\& & \color{blue}{-65} \\ \hline &\color{blue}{-13}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 16 } + \color{orangered}{ \left( -65 \right) } = \color{orangered}{ -49 } $

$$ \begin{array}{c|rr}5&-13&\color{orangered}{ 16 }\\& & \color{orangered}{-65} \\ \hline &\color{blue}{-13}&\color{orangered}{-49} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -13 } $ with a remainder of $ \color{red}{ -49 } $.

Synthetic Division Calculator