To determine which of the given expressions is a trinomial with a constant term, we need to analyze each option carefully.
A trinomial is a polynomial with exactly three terms. Additionally, for our purposes, one of these terms must be a constant term, i.e., a term that does not contain any variables.
Let's examine each option:
1. Option A: [tex]\( x^4 + 3y^2 + 2y \)[/tex]
- This expression has three terms: [tex]\( x^4 \)[/tex], [tex]\( 3y^2 \)[/tex], and [tex]\( 2y \)[/tex].
- However, it does not have a constant term. All terms involve variables.
2. Option B: [tex]\( y^5 + 13x + 12 \)[/tex]
- This expression has three terms: [tex]\( y^5 \)[/tex], [tex]\( 13x \)[/tex], and [tex]\( 12 \)[/tex].
- The term [tex]\( 12 \)[/tex] is a constant term as it does not contain any variables.
- Therefore, this expression is a trinomial and it has a constant term.
3. Option C: [tex]\( x^3 \)[/tex]
- This expression has only one term: [tex]\( x^3 \)[/tex].
- It is not a trinomial since it does not have three terms.
4. Option D: [tex]\( x + 4y \)[/tex]
- This expression has two terms: [tex]\( x \)[/tex] and [tex]\( 4y \)[/tex].
- It is not a trinomial since it does not have three terms.
Given the definitions and the analyses above, the correct answer is:
Option B: [tex]\( y^5 + 13x + 12 \)[/tex]
This option is a trinomial with a constant term (12).
