Select the best answer for the question. Which of the following is a monomial?
A. $2 x-y z$
B. $2+x y z$
C. $2 x y z^2$
D. $2 x+y z$
Answer (2)
A monomial is an expression with only one term.
Option A ( 2 x − yz ) and Option D ( 2 x + yz ) have two terms.
Option B ( 2 + x yz ) has two terms.
Option C ( 2 x y z 2 ) has only one term, thus it is a monomial. C
Explanation
Understanding Monomials A monomial is an algebraic expression consisting of only one term. A monomial can be a number, a variable, or a product of numbers and variables with nonnegative integer exponents. Let's examine each option to determine which one fits this definition.
Analyzing Option A Option A: 2 x − yz has two terms, 2 x and − yz , separated by a subtraction sign. Therefore, it is not a monomial.
Analyzing Option B Option B: 2 + x yz has two terms, 2 and x yz , separated by an addition sign. Therefore, it is not a monomial.
Analyzing Option C Option C: 2 x y z 2 has only one term, which is a product of a constant and variables with nonnegative integer exponents. Therefore, it is a monomial.
Analyzing Option D Option D: 2 x + yz has two terms, 2 x and yz , separated by an addition sign. Therefore, it is not a monomial.
Conclusion Based on our analysis, the only option that is a monomial is C. 2 x y z 2 .
Examples
Monomials are fundamental in algebra and are used in various applications, such as calculating the area of a rectangle ( A = lw , where l is the length and w is the width) or the volume of a cube ( V = s 3 , where s is the side length). Understanding monomials helps in simplifying complex algebraic expressions and solving equations. For instance, if you are calculating the cost of items where each item's price can be represented as a variable, the total cost can be expressed as a monomial.
A monomial is an expression with only one term. Among the options provided, the only monomial is C: 2 x y z 2 . The other options contain two terms and therefore do not qualify as monomials.
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