(a) Complete this synthetic division table.
5) \begin{tabular}{rrrrr}
-1 & 4 & 3 & 8 & 2 \\
& -5 & -5 & -10 & -10 \\
\hline-1 & -1 & -2 & -2 & -8
\end{tabular}
(b) Write your answer in the following form: Quotient $+\frac{\text { Remainder }}{x-5}$.
\[
\frac{-x^{4}+4 x^{3}+3 x^{2}+8 x+2}{x-5}=\llbracket+\frac{\square}{x-5}
\]
Answer
Box the final answer: \n \[\boxed{-x^{3} - x^{2} - 2x - 2 + \frac{-8}{x-5}}\]
Step 1 ：Complete the synthetic division table as follows: \n 5) \begin{tabular}{rrrrr} -1 & 4 & 3 & 8 & 2 \ & -5 & -5 & -10 & -10 \ \hline -1 & -1 & -2 & -2 & -8 \end{tabular}
Step 2 ：Write the answer in the form: Quotient $+\frac{\text{Remainder}}{x-5}$. So, we have: \n \[\frac{-x^{4}+4 x^{3}+3 x^{2}+8 x+2}{x-5}=-x^{3} - x^{2} - 2x - 2 + \frac{-8}{x-5}\]
Step 3 ：Simplify the final answer using Python code. The final answer is: \n \[-x^{3} - x^{2} - 2x - 2 + \frac{-8}{x-5}\]
Step 4 ：Box the final answer: \n \[\boxed{-x^{3} - x^{2} - 2x - 2 + \frac{-8}{x-5}}\]
