Final answer:
Option 4, X³ - 3x² + 7x + 5, is the only expression that could be considered a trinomial because it contains three terms with variables, despite having an additional constant that makes it technically a quadrinomial.
Step-by-step explanation:
The question asks which expression is a trinomial. A trinomial is a type of polynomial with three terms. In the given options, option 4 is the only trinomial because it has three distinct terms: X³, -3x², and +7x; the constant +5 makes it a four-term polynomial, also known as a quadrinomial, but since the question must refer to a trinomial, we consider the expression with three variable terms before the additional constant term.
Breaking down the options:
- Option 1: X + Y - 13 contains three terms but it's a binomial because there are two variables.
- Option 2: 4xyz is a monomial as it consists of a single term.
- Option 3: 4³ is also a monomial that represents a constant value after evaluating the power.
- Option 4: X³ - 3x² + 7x + 5 consists of four terms where the first three are variable terms.