https://file.aiquickdraw.com/mathbot/file/172978278392409peftuu.jpg

Let's analyze each of the algebraic expressions provided and give the best name for each:

1. **\( 6x^7 + 18x^5 - 9x^2 + 17 \)**:
   - The highest power of \( x \) is 7 (degree of the polynomial), so it is a **7th-degree polynomial**. It also contains multiple terms, making it a **polynomial**.

2. **\( 8x^7 + 4 \)**:
   - The highest power of \( x \) is 7. It has two terms, so it is also a **7th-degree binomial** (since it has two terms).

3. **\( 2x^9 \)**:
   - This is a single term with the highest power of \( x \) being 9. It is a **monomial** and a **9th-degree** monomial.

4. **\( 20x^5 - 9x^2 + 16 \)**:
   - The highest power of \( x \) is 5. It contains three terms, so it is a **5th-degree trinomial**.

5. **\( 6x^4 + \frac{7}{x^3} - 18x^2 + 9 \)**:
   - This expression contains terms with negative powers of \( x \) (due to the \( \frac{7}{x^3} \) term). Thus, it is not a standard polynomial but can be classified as a **rational expression** due to the division by \( x^3 \).

Would you like further details or have any questions?

### Related Questions:
1. What makes a polynomial an nth-degree polynomial?
2. How do we differentiate between a binomial and a trinomial?
3. What is a rational expression in algebra?
4. How do terms with negative exponents affect the classification of expressions?
5. Can a monomial ever contain a fraction?

**Tip:** A polynomial's degree is determined by the highest exponent of the variable present in the expression.

For each of the algebraic expressions below, select the BEST name from the list of choices.

Learn how to classify algebraic expressions such as polynomials, binomials, and trinomials. This problem helps students understand how to identify the degree of expressions and how to classify them based on the number of terms. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation