Answer
Quotient = $x^{4}-3x^{3}+5x^{2}-15x+46$
Remainder = $-133 $
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 ($x+3$) ... $c=-3$
\begin{array}{l|ccccc|cc}
-3&1&0&-4&0&1&5&\\
&&-3&9&-15&45&-138&\\ \hline
&1&-3&5&-15&46&-133&\\
\end{array}
Quotient = $x^{4}-3x^{3}+5x^{2}-15x+46$
Remainder = $-133 $
