The image shows a multiple-choice math question asking to select the best name for each algebraic expression listed. I will help break down the expressions and guide you on the naming conventions.

1. $3x^8$

This is a monomial because it consists of a single term.

2. $14x^7 + 18x^4 - 2x^3 + 9$

This is a polynomial with four terms, specifically a quartic polynomial because the highest degree is 7 (a polynomial of degree 7 is called septic or degree-7 polynomial).

3. $15x^4 - 2x^2 + 12$

This is a trinomial because it consists of three terms and has a highest degree of 4.

4. $9x^7 + 2$

This is a binomial since it has two terms and the highest degree is 7 (so it's also a degree-7 binomial).

5. $14x^4 + \frac{7}{x^3} - 18x^2 + 2$

This expression includes a negative power, so it is a rational expression rather than a polynomial.

Would you like more details on how these are categorized? Feel free to ask questions.

Here are 5 related questions to think about:

1. What is the difference between a polynomial and a rational expression?
2. Can you have a monomial with a negative exponent?
3. How do you classify polynomials based on their degree?
4. What makes an algebraic expression a binomial or trinomial?
5. How can you simplify rational expressions?

Tip: When naming algebraic expressions, always focus on the number of terms and the degree (highest exponent).