Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 11 - Rational Expressions and Functions - 11-3 Dividing Polynomials - Practice and Problem-Solving Exercises - Page 671: 59

Answer

$2b^3-2b^2+3$

Work Step by Step

The long division method below shows the result of $ (2b^6+2b^5-4b^4+b^3+8b^2-3)\div(b^3+2b^2-1) .$ $$\begin{array}{l} \phantom{b^3+2b^2-1)}2b^3-2b^2\phantom{-4b^4}\,\,+\phantom{2}3 \\ \color{blue}{b^3+2b^2-1}\color{black}{\overline{\smash{)}2b^6+2b^5-4b^4+\phantom{2}b^3+8b^2-3}} \\ \phantom{b^3+2b^2-1)}\underline{2b^6+4b^5\phantom{-4b^4\,\,}-2b^3} \\ \phantom{b^3+2b^2-1)2b^6}-2b^5-4b^4+3b^3+8b^2 \\ \phantom{b^3+2b^2-1)2b^\,6}\underline{-\,2b^5-4b^4\phantom{+3b^3\,\,}+2b^2} \\ \phantom{b^3+2b^2-1)2b^\,6-2b^5-4b^4+}3b^3+6b^2-3 \\ \phantom{b^3+2b^2-1)2b^\,6-2b^5-4b^4+}\underline{3b^3+6b^2-3} \\ \color{red}{\phantom{b^3+2b^2-1)2b^\,6-2b^5-4b^4+3b^3+6b^2-}0} \end{array}$$Hence, the quotient is $2b^3-2b^2+3$.
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