Find remainder when $ -10x-42 $ is divided by $ x-4 $.

The synthetic division table is:

$$ \begin{array}{c|rr}4&-10&-42\\& & \color{black}{-40} \\ \hline &\color{blue}{-10}&\color{orangered}{-82} \end{array} $$

The remainder when $ -10x-42 $ is divided by $ x-4 $ is $ \, \color{red}{ -82 } $.

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.

$$ \begin{array}{c|rr}\color{blue}{4}&-10&-42\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}4&\color{orangered}{ -10 }&-42\\& & \\ \hline &\color{orangered}{-10}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 4 } \cdot \color{blue}{ \left( -10 \right) } = \color{blue}{ -40 } $.

$$ \begin{array}{c|rr}\color{blue}{4}&-10&-42\\& & \color{blue}{-40} \\ \hline &\color{blue}{-10}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -42 } + \color{orangered}{ \left( -40 \right) } = \color{orangered}{ -82 } $

$$ \begin{array}{c|rr}4&-10&\color{orangered}{ -42 }\\& & \color{orangered}{-40} \\ \hline &\color{blue}{-10}&\color{orangered}{-82} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -82 }\right) $.

Synthetic Division Calculator