College Algebra (10th Edition)

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

Chapter 8 - Section 8.5 - Partial Fraction Decomposition - 8.5 Assess Your Understanding - Page 608: 4

Answer

True

Work Step by Step

By the corollary to the fundamental theorem of algebra, a polynomial of degree n with real coefficients has exactly n complex roots, counting the multiplicity of each root. 1. If c is a real root of the polynomial P(x), then (x-c) is a ${\bf \text{ linear}}$ factor of P(x). 2. If c is a complex root, $c=a+bi$, then its conjugate $\overline{c}=a-bi$ is also a root of P. Both $(x-c)$ and $(x- \overline{c})$ are factors of P: $(x-a-bi)(x-a+bi)=(x-a)^{2}-(bi)^{2}$ $=x^{2}-2ax+a^{2}+b^{2}$, which is a ${\bf \text{quadratic (irreducible)}} $factor of P. The statement is true.
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