College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.6 - Synthetic Division - R.6 Assess Your Understanding - Page 62: 18


Quotient = $x^{4}-x^{3}+x^{2}-x+1$ Remainder = $0$

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&0&0&0&1&\\ &&-1&1&-1&1&-1&\\ \hline &1&-1&1&-1&1&0&\\ \end{array} Quotient = $x^{4}-x^{3}+x^{2}-x+1$ Remainder = $0$
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