Verified Answer :
The first thing you should know for this case is that a monomial is a single term that can be composed of the product of:
1) A coefficient with one or more variables of degree 1.
2) A coefficient with one or more variables of different degrees
For this case, the following expression is a monomial:
\(2xyz ^ 2
\)
The coefficient is 2.
The variables of degree 1 are x and y.
The variable of degree 2 is z.
Answer:
the following is a monomial:
c. \(2xyz^2\)
The correct option is \(\boxed{\bf option (c)}\).
Further explanation:
A monomial is an expression in algebra which contains only one term.
For example: The expression \(3xy\) is a monomial.
Monomial has numbers (real numbers) and variables that are multiplied together.
Option (a)
The expression given in option (a) is \(2x+yz\).
The expression given in option (a) has two terms. So, it is not a monomial.
Therefore, option (a) is incorrect.
Option (b)
The expression given in option (b) is \(2+xyz\).
The expression given in option (b) has two terms. So, it is not a monomial.
Therefore, option (b) is incorrect.
Option (c)
The expression given in option (c) is \(2xyz\).
The expression given in option (c) has only one term. So, it is a monomial.
Therefore, option (c) is correct.
Option (d)
The expression given in option (d) is \(2x-yz\).
The expression given in option (d) has two terms. So, it is not a monomial.
Therefore, option (d) is incorrect.
Thus, the expression \(\boxed{2xyz}\) is a monomial so, the correct option is \(\boxed{\bf option (c)}\).
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Polynomials
Keywords: Monomials, polynomials, binomials, trinomials, algebraic expression, function, sets, real numbers, integers, whole numbers, natural numbers, degree of polynomials, variables.