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 - Practice: 3

Answer

The answers for the Polynomial Types and Degrees are highlighted in the table in blue.
1486093605

Work Step by Step

Each equation given asks for a Polynomial Type and its degree. As shown in the table, Equation (a). $-6x + 14$ is a binomial because it has 2 terms, which are $-6x$ for one and the other is 14. Hence, 2 terms. It is helpful to also remember that the prefix of each Polynomial type each signifies a certain number: In the Polynomial type monomial, its prefix is mono-, meaning 1. So, monomials only have 1 term in an equation. The prefix bi- for binomial means 2. So, binomials have 2 terms in an equation. The prefix tri- for trinomials means 3. So, trinomials have 3 terms in an equation. Based on this, equation (b). $9x$ $- 3x^{6}$ + $5x^{4}$ $+2$ has 4 terms, which means it is neither a monomial, binomial, nor trinomial. But equation (c) $10x^{2}$ – $6x$ $– 6$ has 3 terms, so it is a trinomial. As for degrees, we are looking for the highest exponent listed in each polynomial. For equation (a). $-6x + 14$, the highest exponent is 1. We can rule out the term 14 in the equation, because it is a Constant, and its exponent is 0. So, $-6x$ is the term that provides the highest degree of 1. This is because of $x$. Even though $x$ does not show an exponent visibly, it nevertheless has an assumed degree of 1. Equation (b). 9$x$ $- 3x^{6}$ + $5x^{4}$ $+2$ has 4 terms, so the polynomial's highest degree (exponent) is 6, as seen in its term, $- 3x^{6}$. So, the answer is 6. Equation (c) $10x^{2}$ – $6x$ $– 6$ has 3 terms, and out of those 3, the highest exponent is 2 as seen in its term, $10x^{2}$. So, the trinomial's highest degree (exponent) is 2. So, the answer is 2.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.