Divide using synthetic division $$ ( 6x^{2}+29x+20 ) \div ( x+4 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrr}-4&6&29&20\\& & -24& \color{black}{-20} \\ \hline &\color{blue}{6}&\color{blue}{5}&\color{orangered}{0} \end{array} $$The solution is:
$$ \dfrac{ 6x^{2}+29x+20 }{ x+4 } = \color{blue}{6x+5} $$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.
$$ \begin{array}{c|rrr}\color{blue}{-4}&6&29&20\\& & & \\ \hline &&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrr}-4&\color{orangered}{ 6 }&29&20\\& & & \\ \hline &\color{orangered}{6}&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ 6 } = \color{blue}{ -24 } $.
$$ \begin{array}{c|rrr}\color{blue}{-4}&6&29&20\\& & \color{blue}{-24} & \\ \hline &\color{blue}{6}&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 29 } + \color{orangered}{ \left( -24 \right) } = \color{orangered}{ 5 } $
$$ \begin{array}{c|rrr}-4&6&\color{orangered}{ 29 }&20\\& & \color{orangered}{-24} & \\ \hline &6&\color{orangered}{5}& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ 5 } = \color{blue}{ -20 } $.
$$ \begin{array}{c|rrr}\color{blue}{-4}&6&29&20\\& & -24& \color{blue}{-20} \\ \hline &6&\color{blue}{5}& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ 20 } + \color{orangered}{ \left( -20 \right) } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrr}-4&6&29&\color{orangered}{ 20 }\\& & -24& \color{orangered}{-20} \\ \hline &\color{blue}{6}&\color{blue}{5}&\color{orangered}{0} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 6x+5 } $ with a remainder of $ \color{red}{ 0 } $.