Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - Guided Practice for Example 3 - Page 381: 8



Work Step by Step

The coefficients are rational, thus by the complex conjugates theorem, $3+i$ is also a factor. Using the Factor Theorem if $x=a$ is a factor, then $(x-a)$ is a factor of $f(x)$. Hence here $f(x)=(x-3)(x-(3+i))(x-(3-i))=(x-3)(x-3-i)(x-3+i))=(x-3)((x-3)^2-i^2)=(x-3)(x^2-6x+10)=x^3-6x^2+10x-3x^2+18x-30=x^3-9x^2+28x-30$
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