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.
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Dividing with ($x-2$) $\qquad$... $c=2.$
\begin{array}{l|ccc|cc}
2&4&-3&-8&4&&&\\
&&8&10&4&&&\\ \hline
&4&5&2&8&&&\\
\end{array}
The remainder is 8, ($x-2$) is not a factor of P(x).
