Divide using synthetic division $$ ( 4.9x-3 ) \div ( x-1 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}1&\frac{ 49 }{ 10 }&-3\\& & \color{black}{\frac{ 49 }{ 10 }} \\ \hline &\color{blue}{\frac{ 49 }{ 10 }}&\color{orangered}{\frac{ 19 }{ 10 }} \end{array} $$

The solution is:

$$ \frac{ \frac{ 49 }{ 10 }x-3 }{ x-1 } = \color{blue}{\frac{ 49 }{ 10 }} ~+~ \frac{ \color{red}{ \frac{ 19 }{ 10 } } }{ x-1 } $$

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.

$$ \begin{array}{c|rr}\color{blue}{1}&\frac{ 49 }{ 10 }&-3\\& & \\ \hline && \end{array} $$

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

$$ \begin{array}{c|rr}1&\color{orangered}{ \frac{ 49 }{ 10 } }&-3\\& & \\ \hline &\color{orangered}{\frac{ 49 }{ 10 }}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ \frac{ 49 }{ 10 } } = \color{blue}{ \frac{ 49 }{ 10 } } $.

$$ \begin{array}{c|rr}\color{blue}{1}&\frac{ 49 }{ 10 }&-3\\& & \color{blue}{\frac{ 49 }{ 10 }} \\ \hline &\color{blue}{\frac{ 49 }{ 10 }}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -3 } + \color{orangered}{ \frac{ 49 }{ 10 } } = \color{orangered}{ \frac{ 19 }{ 10 } } $

$$ \begin{array}{c|rr}1&\frac{ 49 }{ 10 }&\color{orangered}{ -3 }\\& & \color{orangered}{\frac{ 49 }{ 10 }} \\ \hline &\color{blue}{\frac{ 49 }{ 10 }}&\color{orangered}{\frac{ 19 }{ 10 }} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ \frac{ 49 }{ 10 } } $ with a remainder of $ \color{red}{ \frac{ 19 }{ 10 } } $.

Synthetic Division Calculator