College Algebra (10th Edition)

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

Chapter 5 - Section 5.1 - Polynomial Functions and Models - 5.1 Assess Your Understanding: 28

Answer

It is a polynomial. Degree: 5 Leading term: $-3x^5$ Constant: 0 $G(x) = -3x^5 -18x^4 -36x^3 -24x^2$

Work Step by Step

First, we simplify: $$ G(x)= -3x^2 (x+2)^3 \\G(x) = -3x^2 (x^{2} +4x +4) (x+2)^3 \\ G(x) = -3x^5 -18x^4 -36x^3 -24x^2$$ By definition, a polynomial is a function containing only terms where x is raised to a positive, integer power or constants. This is true, so we see that it is a polynomial. The degree is equal to the exponent of the term with the highest exponent, so the degree is 5. The term that has the highest degree, $-3x^5$, is always the leading term. Finally, there is no constant, so we call the constant 0.
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