3. Classify each polynomial and state its degree. 
a) -4a⁶bc²
b) 2p³q²+3p⁴q

Let's classify each polynomial and state its degree:

### a) \(-4a^6bc^2\)
- **Classification**: This is a **monomial**, since it consists of a single term.
- **Degree**: The degree of a monomial is the sum of the exponents of its variables. In this case:
  - \(a^6\) has an exponent of 6,
  - \(b\) has an exponent of 1 (implied),
  - \(c^2\) has an exponent of 2.
  - Sum: \(6 + 1 + 2 = 9\).
  
  **Degree**: 9.

### b) \(2p^3q^2 + 3p^4q\)
- **Classification**: This is a **binomial**, since it consists of two terms.
- **Degree**: For each term, the degree is the sum of the exponents of the variables:
  - For the first term \(2p^3q^2\), the degree is:
    - \(p^3\) has an exponent of 3,
    - \(q^2\) has an exponent of 2.
    - Sum: \(3 + 2 = 5\).
  - For the second term \(3p^4q\), the degree is:
    - \(p^4\) has an exponent of 4,
    - \(q\) has an exponent of 1 (implied).
    - Sum: \(4 + 1 = 5\).
  
  Since both terms have a degree of 5, the **degree of the binomial is 5** (the highest degree term).

---

Would you like more details or have any questions about the classifications or degrees?

### Related Questions:
1. What is the difference between a monomial, binomial, and trinomial?
2. How do you find the degree of a polynomial with multiple variables?
3. What happens if a polynomial has no exponents on certain variables?
4. How would the classification change if a polynomial had three terms instead of two?
5. How do coefficients affect the classification or degree of a polynomial?

**Tip**: The degree of a polynomial is always determined by the term with the highest sum of exponents.

Classify each polynomial and state its degree. a) -4a⁶bc² b) 2p³q²+3p⁴q

Understand how to classify polynomials and calculate their degree. This example includes a monomial -4a⁶bc² and a binomial 2p³q²+3p⁴q. Learn key algebra concepts and how to find the degree of each term. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation