Answer
Quotient =$x^{4}-x^{3}+6x^{2}-6x+6$
Remainder = $-16$
Work Step by Step
Dividing a polynomial P(x) with (x-c) using synthetic division:
Set up a table in three rows:
1. 1st row: place c, followed by coefficients of the powers of x (do not skip zeros)
2. third row, : copy the leading coefficient (call it A)
3. The entry of the middle row in the next column is obtained by multiplying A with c.
4. The next entry of the third row is obtained by adding the two entries in rows 1 and 2.
5. Repeat steps 3 and 4 until the table is filled.
Interpret the result:
the last entry of the last row gives the remainder, and
the preceding entries are coefficients of the quotient.
----
Dividing with ($x+1$) $\qquad$... $c=-1$
\begin{array}{l|ccccc|cc}
-1&1&0&5&0&0&-10&\\
&&-1&1&-6&6&-6&\\\hline
&1&-1&6&-6&6&-16&\\
\end{array}
Quotient =$x^{4}-x^{3}+6x^{2}-6x+6$
Remainder = $-16$
