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: 25

Answer

It is a polynomial. Degree: 4 Leading term: $5x^4$ Constant: $\frac{1}{2}$ $5x^4- \pi x^3+.5$

Work Step by Step

By definition, a polynomial is a function containing only terms where x is raised to a positive, integer power or constants. x is raised to the third power, x is raised to the fourth power, and $\frac{1}{2}$ is a constant, 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 4. The term that has the highest degree, $5x^4$, is always the leading term. Finally, $\frac{1}{2}$ is a constant.
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