Find remainder when $ -35x+53 $ is divided by $ 5x-4 $.

The synthetic division table is:

$$ \begin{array}{c|rr}4&-35&53\\& & \color{black}{-140} \\ \hline &\color{blue}{-35}&\color{orangered}{-87} \end{array} $$

The remainder when $ -35x+53 $ is divided by $ x-4 $ is $ \, \color{red}{ -87 } $.

We can find remainder using synthetic division method.

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.

$$ \begin{array}{c|rr}\color{blue}{4}&-35&53\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}4&\color{orangered}{ -35 }&53\\& & \\ \hline &\color{orangered}{-35}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 4 } \cdot \color{blue}{ \left( -35 \right) } = \color{blue}{ -140 } $.

$$ \begin{array}{c|rr}\color{blue}{4}&-35&53\\& & \color{blue}{-140} \\ \hline &\color{blue}{-35}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 53 } + \color{orangered}{ \left( -140 \right) } = \color{orangered}{ -87 } $

$$ \begin{array}{c|rr}4&-35&\color{orangered}{ 53 }\\& & \color{orangered}{-140} \\ \hline &\color{blue}{-35}&\color{orangered}{-87} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -87 }\right) $.

Synthetic Division Calculator