To determine which expression is a trinomial, let's start by understanding what a trinomial is.
A trinomial is a type of polynomial that consists of exactly three terms. Each term in a polynomial is separated by a plus (+) or minus (-) sign.
Let's examine the given expressions one by one:
1. Expression: [tex]\(x + y - 13\)[/tex]
- This expression has three terms: [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(-13\)[/tex].
- Since it has exactly three terms, this is a trinomial.
2. Expression: [tex]\(4xyz\)[/tex]
- This expression has only one term, which is [tex]\(4xyz\)[/tex].
- Since it has only one term, it is a monomial, not a trinomial.
3. Expression: [tex]\(4x^3\)[/tex]
- This expression also has only one term, which is [tex]\(4x^3\)[/tex].
- Since it has only one term, it is a monomial, not a trinomial.
4. Expression: [tex]\(x^3 - 3x^2 + 7x + 5\)[/tex]
- This expression has four terms: [tex]\(x^3\)[/tex], [tex]\(-3x^2\)[/tex], [tex]\(7x\)[/tex], and [tex]\(5\)[/tex].
- Since it has four terms, it is a polynomial with four terms, not a trinomial.
From the analysis of each expression, the trinomial among the given options is the expression:
[tex]\[ x + y - 13 \][/tex]
Thus, the correct answer is the expression at position 1:
[tex]\[ x + y - 13 \][/tex]
