College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.3 - Page 374: 24

Answer

$ x^{4}+7x^{3}+21x^{2}+60x+182+\displaystyle \frac{549}{x-3}$

Work Step by Step

Synthetic Division To divide a polynomial by $x-c$: 1. Arrange the polynomial in descending powers, with a $0$ coefficient for any missing term. 2. Write $c$ for the divisor, $x-c$. To the right, write the coefficients of the dividend. 3. Write the leading coefficient of the dividend on the bottom row 4. Multiply $c$ times the value just written on the bottom row. Write the product in the next column in the second row. 5. Add the values in this new column, writing the sum in the bottom row. 6. Repeat this series of multiplications and additions until all columns are filled in. 7. Use the numbers in the last row to write the quotient, plus the remainder above the divisor. The degree of the first term of the quotient is one less than the degree of the first term of the dividend. The final value in this row is the remainder. ---------------------------- (watch out for the missing $\mathrm{x}^{3}$ term) $\begin{array}{lllllll} \underline{3}| & 1 & 4 & 0 & -3 & 2 & 3\\ & & 3 & 21 & 63 & 180 & 546\\ & -- & -- & -- & -- & -- & --\\ & 1 & 7 & 21 & 60 & 182 & 549 \end{array}$ $(x^{5}+4x^{4}+21x^{2}+60x+181)\div(x-3)= $ $= x^{4}+7x^{3}+21x^{2}+60x+182+\displaystyle \frac{549}{x-3}$
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