Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.3 - Introduction to Polynomials - Vocabulary and Readiness Check: 6

Answer

"The degree of a polynomial is the greatest degree of any term of the polynomial." The answer is "greatest."

Work Step by Step

The answer to problem #6 is: "The degree of a polynomial is the greatest degree of any term of the polynomial." So, the answer is "greatest." The "greatest" degree of a polynomial is referring to its largest, or highest, exponent. Example: $x^{2} + 4x + 3$ Looking at the exponents of the terms in the example, there is only one exponent that is visible, while other exponents are merely "understood," or simplified. So, if we separate the polynomial by its terms, while also writing in the "understood" exponents, we get: Term #1: $x^{2}$, which has an exponent of $2$. Term #2: $4x^{1}$, which has an exponent of $1$. Term #3: $3^{1}$, which has an exponent of $1$. Term #1 has the greatest/highest exponent, so the answer to this example would be $2$. Thus, the answer to problem #6 is "greatest."
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