Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Concept and Vocabulary Check - Page 377: 7


The Linear Factorization Theorem states that an nth-degree polynomial can be expressed as the product of a nonzero constant and n linear factors, where each linear factor has a leading coefficient of 1.

Work Step by Step

According to the linear factorization theorem, if $f\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+...+{{a}_{1}}x+{{a}_{0}}$, such that $n\ge 1$ and ${{a}_{n}}\ne 0$, then $f\left( x \right)={{a}_{n}}\left( x-{{c}_{1}} \right)\left( x-{{c}_{2}} \right)...\left( x-{{c}_{n}} \right)$. Here, ${{c}_{1}}, {{c}_{2}}\text{,} ... \text{,} {{c}_{n}}$ are complex numbers, which can possibly be real as well as non-distinct. Also, $\left( x-{{c}_{1}} \right), \left( x-{{c}_{2}} \right), ..., \left( x-{{c}_{n}} \right)$ are called linear factors because their degree is 1. Hence, the given statement is the same as above, but expressed in words.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.