Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 208: 25

Answer

It is a polynomial $G(x) =2x^4-4x^3+4x^2-4x+2$ of degree: $4$ Leading term: $2x^4$ Constant: $2$

Work Step by Step

We re-arrange the given function as follows: $ G(x)= 2 (x-1)^2 (x^2+1) \\ =2x^4-4x^3+4x^2-4x+2$ A polynomial can be defined as a function containing only terms where $x$ is raised to a positive, integer power or constant. We can see from the given function that it is a polynomial. The degree is equal to the power of the term with the highest power, so the degree is $4$. Also, the constant value is $2$. The term with the highest degree is always known as the leading term; that is, $2x^4$. It is a polynomial $G(x) =2x^4-4x^3+4x^2-4x+2$ of degree: $4$ Leading term: $2x^4$ Constant: $2$
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