Divide using synthetic division $$ ( 17x^{2}+23x-40 ) \div ( x-1 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrr}1&17&23&-40\\& & 17& \color{black}{40} \\ \hline &\color{blue}{17}&\color{blue}{40}&\color{orangered}{0} \end{array} $$The solution is:
$$ \dfrac{ 17x^{2}+23x-40 }{ x-1 } = \color{blue}{17x+40} $$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.
$$ \begin{array}{c|rrr}\color{blue}{1}&17&23&-40\\& & & \\ \hline &&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrr}1&\color{orangered}{ 17 }&23&-40\\& & & \\ \hline &\color{orangered}{17}&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ 17 } = \color{blue}{ 17 } $.
$$ \begin{array}{c|rrr}\color{blue}{1}&17&23&-40\\& & \color{blue}{17} & \\ \hline &\color{blue}{17}&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 23 } + \color{orangered}{ 17 } = \color{orangered}{ 40 } $
$$ \begin{array}{c|rrr}1&17&\color{orangered}{ 23 }&-40\\& & \color{orangered}{17} & \\ \hline &17&\color{orangered}{40}& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ 40 } = \color{blue}{ 40 } $.
$$ \begin{array}{c|rrr}\color{blue}{1}&17&23&-40\\& & 17& \color{blue}{40} \\ \hline &17&\color{blue}{40}& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ -40 } + \color{orangered}{ 40 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrr}1&17&23&\color{orangered}{ -40 }\\& & 17& \color{orangered}{40} \\ \hline &\color{blue}{17}&\color{blue}{40}&\color{orangered}{0} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 17x+40 } $ with a remainder of $ \color{red}{ 0 } $.