College Algebra (10th Edition)

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

Chapter R - Section R.5 - Polynomials - R.4 Assess Your Understanding - Page 49: 103

Answer

Quotient: $x^2-x-1$ Remainder: $2x+2$

Work Step by Step

$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space$ $\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space$ $x^2-x-1$ $x^2+x+1$$\space)\overline{x^4+0x^3-x^2+0x+1}$ $\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{x^4\space+x^3\space+x^2}$ $\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space-x^3-2x^2+0x$ $\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{-x^3-x^2\space\space-x}$ $\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space-x^2+x+1$ $\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{-x^2-x-1}$ $\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space2x+2$ Check answer: $(x^2-x-1)\cdot(x^2+x+1)+2x+2$ $x^4+x^3+x^2-x^3-x^2-x-x^2-x-1+2x+2$ $x^4-x^2+1\checkmark$
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