Divide using synthetic division $$ ( 12x^{2}+37x-11 ) \div ( x-3 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrr}3&12&37&-11\\& & 36& \color{black}{219} \\ \hline &\color{blue}{12}&\color{blue}{73}&\color{orangered}{208} \end{array} $$The solution is:
$$ \dfrac{ 12x^{2}+37x-11 }{ x-3 } = \color{blue}{12x+73} ~+~ \dfrac{ \color{red}{ 208 } }{ x-3 } $$Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -3 = 0 $ ( $ x = \color{blue}{ 3 } $ ) at the left.
$$ \begin{array}{c|rrr}\color{blue}{3}&12&37&-11\\& & & \\ \hline &&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrr}3&\color{orangered}{ 12 }&37&-11\\& & & \\ \hline &\color{orangered}{12}&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ 12 } = \color{blue}{ 36 } $.
$$ \begin{array}{c|rrr}\color{blue}{3}&12&37&-11\\& & \color{blue}{36} & \\ \hline &\color{blue}{12}&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 37 } + \color{orangered}{ 36 } = \color{orangered}{ 73 } $
$$ \begin{array}{c|rrr}3&12&\color{orangered}{ 37 }&-11\\& & \color{orangered}{36} & \\ \hline &12&\color{orangered}{73}& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ 73 } = \color{blue}{ 219 } $.
$$ \begin{array}{c|rrr}\color{blue}{3}&12&37&-11\\& & 36& \color{blue}{219} \\ \hline &12&\color{blue}{73}& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ -11 } + \color{orangered}{ 219 } = \color{orangered}{ 208 } $
$$ \begin{array}{c|rrr}3&12&37&\color{orangered}{ -11 }\\& & 36& \color{orangered}{219} \\ \hline &\color{blue}{12}&\color{blue}{73}&\color{orangered}{208} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 12x+73 } $ with a remainder of $ \color{red}{ 208 } $.