https://file.aiquickdraw.com/mathbot/file/1729805356492pou5kguf.jpg

To determine the degree of the polynomial:

\[
3a^8b^5 - 9a^6b^6 + 5ab + 7
\]

The degree of a polynomial is the highest sum of the exponents of variables in any of its terms. Let's break down each term:

1. \( 3a^8b^5 \) has the exponents of \(a = 8\) and \(b = 5\). The sum is \(8 + 5 = 13\).
2. \( -9a^6b^6 \) has the exponents of \(a = 6\) and \(b = 6\). The sum is \(6 + 6 = 12\).
3. \( 5ab \) has the exponents of \(a = 1\) and \(b = 1\). The sum is \(1 + 1 = 2\).
4. The constant \(7\) has no variables, so its degree is 0.

The highest sum of exponents is \(13\), so the degree of the polynomial is **13**.

The correct answer is **A. 13**.

Would you like further details or have any questions?

Here are five related questions:
1. How do you find the degree of a term in a polynomial?
2. What is the degree of a constant term in a polynomial?
3. How does the degree of a polynomial affect its graph?
4. What is the difference between the degree of a polynomial and the number of terms?
5. Can two different terms in a polynomial have the same degree?

**Tip**: Always check the highest sum of exponents when determining the degree of a polynomial.

Determine the degree of the polynomial: 3a^8b^5 - 9a^6b^6 + 5ab + 7

Learn how to determine the degree of the polynomial 3a^8b^5 - 9a^6b^6 + 5ab + 7. This problem focuses on finding the highest sum of exponents from each term, ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation