The synthetic division table is:
$$ \begin{array}{c|rrrrr}1&4&-7&9&4&-10\\& & 4& -3& 6& \color{black}{10} \\ \hline &\color{blue}{4}&\color{blue}{-3}&\color{blue}{6}&\color{blue}{10}&\color{orangered}{0} \end{array} $$The solution is:
$$ \frac{ 4x^{4}-7x^{3}+9x^{2}+4x-10 }{ x-1 } = \color{blue}{4x^{3}-3x^{2}+6x+10} $$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.
$$ \begin{array}{c|rrrrr}\color{blue}{1}&4&-7&9&4&-10\\& & & & & \\ \hline &&&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrrr}1&\color{orangered}{ 4 }&-7&9&4&-10\\& & & & & \\ \hline &\color{orangered}{4}&&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ 4 } = \color{blue}{ 4 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{1}&4&-7&9&4&-10\\& & \color{blue}{4} & & & \\ \hline &\color{blue}{4}&&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ -7 } + \color{orangered}{ 4 } = \color{orangered}{ -3 } $
$$ \begin{array}{c|rrrrr}1&4&\color{orangered}{ -7 }&9&4&-10\\& & \color{orangered}{4} & & & \\ \hline &4&\color{orangered}{-3}&&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ \left( -3 \right) } = \color{blue}{ -3 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{1}&4&-7&9&4&-10\\& & 4& \color{blue}{-3} & & \\ \hline &4&\color{blue}{-3}&&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ 9 } + \color{orangered}{ \left( -3 \right) } = \color{orangered}{ 6 } $
$$ \begin{array}{c|rrrrr}1&4&-7&\color{orangered}{ 9 }&4&-10\\& & 4& \color{orangered}{-3} & & \\ \hline &4&-3&\color{orangered}{6}&& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ 6 } = \color{blue}{ 6 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{1}&4&-7&9&4&-10\\& & 4& -3& \color{blue}{6} & \\ \hline &4&-3&\color{blue}{6}&& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ 4 } + \color{orangered}{ 6 } = \color{orangered}{ 10 } $
$$ \begin{array}{c|rrrrr}1&4&-7&9&\color{orangered}{ 4 }&-10\\& & 4& -3& \color{orangered}{6} & \\ \hline &4&-3&6&\color{orangered}{10}& \end{array} $$Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 1 } \cdot \color{blue}{ 10 } = \color{blue}{ 10 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{1}&4&-7&9&4&-10\\& & 4& -3& 6& \color{blue}{10} \\ \hline &4&-3&6&\color{blue}{10}& \end{array} $$Step 9 : Add down last column: $ \color{orangered}{ -10 } + \color{orangered}{ 10 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrrrr}1&4&-7&9&4&\color{orangered}{ -10 }\\& & 4& -3& 6& \color{orangered}{10} \\ \hline &\color{blue}{4}&\color{blue}{-3}&\color{blue}{6}&\color{blue}{10}&\color{orangered}{0} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 4x^{3}-3x^{2}+6x+10 } $ with a remainder of $ \color{red}{ 0 } $.