Find remainder when $ 80x-30 $ is divided by $ 2x+1 $.

The synthetic division table is:

$$ \begin{array}{c|rr}-1&80&-30\\& & \color{black}{-80} \\ \hline &\color{blue}{80}&\color{orangered}{-110} \end{array} $$

The remainder when $ 80x-30 $ is divided by $ x+1 $ is $ \, \color{red}{ -110 } $.

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 + 1 = 0 $ ( $ x = \color{blue}{ -1 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{-1}&80&-30\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}-1&\color{orangered}{ 80 }&-30\\& & \\ \hline &\color{orangered}{80}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ 80 } = \color{blue}{ -80 } $.

$$ \begin{array}{c|rr}\color{blue}{-1}&80&-30\\& & \color{blue}{-80} \\ \hline &\color{blue}{80}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -30 } + \color{orangered}{ \left( -80 \right) } = \color{orangered}{ -110 } $

$$ \begin{array}{c|rr}-1&80&\color{orangered}{ -30 }\\& & \color{orangered}{-80} \\ \hline &\color{blue}{80}&\color{orangered}{-110} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -110 }\right) $.

Synthetic Division Calculator