Let's analyze each option to determine which one is a trinomial with a constant term:
A. [tex]\( y^6 + 8y^3 + 64y \)[/tex]
- This expression is a polynomial, but it only contains terms that have the variable [tex]\(y\)[/tex] with different exponents. A trinomial is a polynomial with exactly three terms, which this has, but it does not include a constant term (a term with no variable), so it doesn't fit the requirement fully.
B. [tex]\( x + 2y + 10 \)[/tex]
- This expression is a trinomial because it has exactly three terms: [tex]\(x\)[/tex], [tex]\(2y\)[/tex], and the constant term [tex]\(10\)[/tex]. Furthermore, it includes a constant term (10), which makes it meet the criteria specified in the question.
C. [tex]\( x \)[/tex]
- This is not a trinomial. It is a monomial (a polynomial with only one term).
D. [tex]\( x^3 + y \)[/tex]
- While this expression has two terms, it does not have a constant term. It is a binomial, not a trinomial.
Considering all the options, the correct trinomial with a constant term is:
B. [tex]\( x + 2y + 10 \)[/tex]
