To determine which of the given options is a monomial, we need to understand the definition of a monomial. A monomial is an algebraic expression that consists of only one term. This term can be a constant, a variable, or a product of constants and variables with non-negative integer exponents. Importantly, a monomial does not contain addition or subtraction operators separating different terms.
Let's analyze each option:
A. [tex]\(2x + yz\)[/tex]
- This expression contains two terms: [tex]\(2x\)[/tex] and [tex]\(yz\)[/tex].
- These terms are separated by the addition operator (+).
- Therefore, this is not a monomial.
B. [tex]\(2 + xyz\)[/tex]
- This expression also contains two terms: [tex]\(2\)[/tex] and [tex]\(xyz\)[/tex].
- These terms are separated by the addition operator (+).
- Thus, this is not a monomial.
C. [tex]\(2xyz^2\)[/tex]
- This expression consists of only one term.
- It is a product of the constant [tex]\(2\)[/tex], and variables [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z^2\)[/tex].
- There are no addition or subtraction operators separating different terms.
- Therefore, this is a monomial.
D. [tex]\(2x - yz\)[/tex]
- This expression contains two terms: [tex]\(2x\)[/tex] and [tex]\(yz\)[/tex].
- These terms are separated by the subtraction operator (-).
- Therefore, this is not a monomial.
Given this analysis, only option C. [tex]\(2xyz^2\)[/tex] is a monomial as it meets the criteria of containing a single term without any addition or subtraction.
Hence, the correct option is:
3. [tex]\(2xyz^2\)[/tex]
