College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Concept and Vocabulary Check: 1

Answer

Degree = $5$ Leading Coefficient = $-2$

Work Step by Step

To find the degree of a polynomial function, we must find the variable with the highest exponent. For this, we must expand the function given: $$f(x) = -2x^3 (x - 1)(x + 5)$$ $$f(x) = -2x^3 (x^2 - x + 5x - 5)$$ $$f(x) = -2x^5 - 4x^4 + 10x^3$$ We can now say that the degree of the polynomial is $5$. The leading coefficient is the coefficient next to the variable with the highest exponent, therefore, it is $-2$.
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