Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 11 - Rational Expressions and Functions - 11-3 Dividing Polynomials - Practice and Problem-Solving Exercises - Page 681: 9


$3x^4 - \frac{2}{x}$

Work Step by Step

Given: $(12x^8 - 8x^3) \div 4x^4$ $(12x^8 - 8x^3) \div 4x^4 = \frac{12x^8}{4x^4} - \frac{8x^3}{4x^4}$ (distributive law) Next, separate the coefficient from the x terms. $\frac{12x^8}{4x^4} - \frac{8x^3}{4x^4} = (\frac{12}{4})(\frac{x^8}{x^4}) - (\frac{8}{4})(\frac{x^3}{x^4})$ $= (3)(x^{8-4}) - (2)(x^{3-4})$ (Use the second law of indices with the same base: $a^{m} \div a^{y} = a^{m-n}$ $= (3)(x^4) - (2)(x^{-1})$ Convert all terms to a positive index. $= 3x^4 - \frac{2}{x}$
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