1. The problem is to classify each given expression as a monomial, binomial, trinomial, or neither. 2. Definitions: - A **monomial** is a single term consisting of numbers and variables multiplied together. - A **binomial** has exactly two terms separated by plus or minus signs. - A **trinomial** has exactly three terms. - Anything with more than three terms or expressions that are not polynomials is classified as **neither**. 3. Classify each expression: - $7x^3 - 3x^2 + 5x - 11$: This has four terms, so it is **neither**. - $7x^3 - 3x^2 + 5$: This has three terms, so it is a **trinomial**. - $\frac{3x^2}{7}$: This is a single term (monomial) because division by a constant is allowed in monomials. - $\frac{2}{3}x + \frac{7}{11}$: Two terms, so it is a **binomial**. - $7x^3 y z^2$: One term with multiple variables multiplied, so it is a **monomial**. - $\frac{x - 1}{2x^2 + 3}$: This is a rational expression (a fraction of polynomials), not a polynomial term, so **neither**. - $7x^3 - 11y z^2$: Two terms, so it is a **binomial**. 4. Summary: - $7x^3 - 3x^2 + 5x - 11$: Neither - $7x^3 - 3x^2 + 5$: Trinomial - $\frac{3x^2}{7}$: Monomial - $\frac{2}{3}x + \frac{7}{11}$: Binomial - $7x^3 y z^2$: Monomial - $\frac{x - 1}{2x^2 + 3}$: Neither - $7x^3 - 11y z^2$: Binomial This classification helps understand the structure of algebraic expressions and is useful for simplifying and solving equations.