https://file.aiquickdraw.com/mathbot/file/1730520026084v6yx3tcc.jpg

To solve each of these questions, let's go through them one by one, focusing on the degree of each term and the polynomial.

### 1. Find the degree of the term \(3x^6\):
- The degree of a term with one variable is the exponent of the variable. Here, the exponent of \(x\) is 6.
- **Answer:** The degree of \(3x^6\) is 6.

### 2. Find the degree of the term \(-4\):
- The term \(-4\) is a constant, and constants have a degree of 0.
- **Answer:** The degree of \(-4\) is 0.

### 3. Find the degree of the term \(-5x^9\):
- The exponent of \(x\) in \(-5x^9\) is 9.
- **Answer:** The degree of \(-5x^9\) is 9.

### 4. Find the degree of the term \(4x^8\):
- The exponent of \(x\) in \(4x^8\) is 8.
- **Answer:** The degree of \(4x^8\) is 8.

### 5. Find the degree of the polynomial \(3x^6 - 4 - 5x^9 + 4x^8\):
- The degree of a polynomial is the highest degree of any individual term within it.
- The degrees of the terms are:
  - \(3x^6\): 6
  - \(-4\): 0
  - \(-5x^9\): 9
  - \(4x^8\): 8
- The highest degree among these terms is 9.
- **Answer:** The degree of the polynomial \(3x^6 - 4 - 5x^9 + 4x^8\) is 9.

Let me know if you'd like more details or have questions on any step.

---

### Related Questions:
1. What is the degree of a polynomial with terms that all have the same degree?
2. How does the degree of a constant term compare to variable terms?
3. How do we determine the degree of a polynomial with multiple variables?
4. Why is the degree of a constant term always 0?
5. What is the effect of adding or subtracting terms on the degree of a polynomial?

### Tip:
The degree of a polynomial is always determined by the term with the highest power of the variable, even if it's negative or involves a coefficient.

Find the degrees of individual terms and the polynomial: 3x^6, -4, -5x^9, 4x^8, and 3x^6 - 4 - 5x^9 + 4x^8.

Learn how to find the degrees of individual terms and the entire polynomial expression 3x^6 - 4 - 5x^9 + 4x^8. This tutorial covers key algebraic concepts like polynomial degree, exponents, and constant terms, making it ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation