Answer
No.
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.
$(x-c)$ is a factor if the remainder is 0.
----
Dividing with ($x+\displaystyle \frac{1}{3}$) $\qquad$... $c=-\displaystyle \frac{1}{3}. $
\begin{array}{r|rrrr|r}
- 1/3 & 3 & 1 & 0 & -3 & 1 \\
& & -1 & -0 & 0 & 1 \\ \hline
& 3 & 0 & -0 & -3 & 2 \\
\end{array}
The remainder is not 0,$\qquad$... ($x+1/3$) is not a factor of P(x)
