Divide using synthetic division $$ ( 6x^{3}+59x^{2}+146x-26 ) \div ( 0.1666666666 ) $$
Answer
The synthetic division table is:
$$ \begin{array}{c|rrrr}0&6&59&146&-26\\& & 0& 0& \color{black}{0} \\ \hline &\color{blue}{6}&\color{blue}{59}&\color{blue}{146}&\color{orangered}{-26} \end{array} $$The solution is:
$$ \frac{ 6x^{3}+59x^{2}+146x-26 }{ x } = \color{blue}{6x^{2}+59x+146} \color{red}{~-~} \frac{ \color{red}{ 26 } }{ x } $$Explanation
Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.
$$ \begin{array}{c|rrrr}\color{blue}{0}&6&59&146&-26\\& & & & \\ \hline &&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrr}0&\color{orangered}{ 6 }&59&146&-26\\& & & & \\ \hline &\color{orangered}{6}&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 6 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&6&59&146&-26\\& & \color{blue}{0} & & \\ \hline &\color{blue}{6}&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 59 } + \color{orangered}{ 0 } = \color{orangered}{ 59 } $
$$ \begin{array}{c|rrrr}0&6&\color{orangered}{ 59 }&146&-26\\& & \color{orangered}{0} & & \\ \hline &6&\color{orangered}{59}&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 59 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&6&59&146&-26\\& & 0& \color{blue}{0} & \\ \hline &6&\color{blue}{59}&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ 146 } + \color{orangered}{ 0 } = \color{orangered}{ 146 } $
$$ \begin{array}{c|rrrr}0&6&59&\color{orangered}{ 146 }&-26\\& & 0& \color{orangered}{0} & \\ \hline &6&59&\color{orangered}{146}& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 146 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&6&59&146&-26\\& & 0& 0& \color{blue}{0} \\ \hline &6&59&\color{blue}{146}& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ -26 } + \color{orangered}{ 0 } = \color{orangered}{ -26 } $
$$ \begin{array}{c|rrrr}0&6&59&146&\color{orangered}{ -26 }\\& & 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{6}&\color{blue}{59}&\color{blue}{146}&\color{orangered}{-26} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 6x^{2}+59x+146 } $ with a remainder of $ \color{red}{ -26 } $.