Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - 3.2 - Polynomial Functions of Higher Degree - 3.2 Exercises - Page 261: 61



Work Step by Step

$f(x)=a(x-2)[x-(2+\sqrt 5)][x-(2-\sqrt 5)]=a(x-2)[(x-2)-\sqrt 5][(x-2)+\sqrt 5]=a(x-2)[(x-2)^2-(\sqrt 5)^2]=a(x-2)(x^2-4x+4-5)=a(x-2)(x^2-4x-1)=a(x^3-6x^2+7x+2)$ $a$ can be any value. If $a=1$: $f(x)=x^3-6x^2+7x+2$
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