Answer
Quotient = $x^{2}+x-4$
Remainder = $5$
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) ... $c=-1$
\begin{array}{l|rrrr|r}
-1 & & 1 & 2 & -3 & 1 \\
& & & -1 & -1 & 4 \\
\hline
& & 1 & 1 & -4 & 5 \\
\end{array}
Quotient = $x^{2}+x-4$
Remainder = $5$
