Given:
[tex]\begin{gathered} -x^2+x-7 \\ x+1 \end{gathered}[/tex]Required:
To find the quotient and remainder using synthetic division.
Explanation:
Consider
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} -1|-1\text{ }+1\text{ }-7 \\ \text{ }|\text{ }+1\text{ }-2 \\ ------------------- \\ \text{ }-1\text{ }+2\text{ }-9 \\ \end{gathered}[/tex][tex]-x+2-\frac{9}{x+1}[/tex]Here the quotient is
[tex]-x+2[/tex]And the remainder is
[tex]-9[/tex]Final Answer:
Quotient :
[tex]-x+2[/tex]Remainder : -9.
