Which of the following is a monomial?
A. $11 x-9$
B. $\frac{9}{\square}$
C. $20 x^9-7 x$
D. $20 x^9$
Answer (1)
A monomial is an algebraic expression with only one term and non-negative integer exponents.
Option A ( 11 x − 9 ) and Option C ( 20 x 9 − 7 x ) are binomials (two terms).
Option B ( □ 9 ) has a negative exponent, so it's not a monomial.
Option D ( 20 x 9 ) fits the definition of a monomial, so the final answer is D .
Explanation
Understanding Monomials Let's analyze each option to determine which one is a monomial. A monomial is an algebraic expression consisting of only one term. This term can be a constant, a variable, or a product of constants and variables. The variables must have non-negative integer exponents.
Analyzing Option A Option A: 11 x − 9 has two terms, 11 x and − 9 . Therefore, it is not a monomial. It is a binomial.
Analyzing Option B Option B: □ 9 can be written as 9 x − 1 . Since the exponent of the variable x is − 1 , which is a negative integer, this is not a monomial.
Analyzing Option C Option C: 20 x 9 − 7 x has two terms, 20 x 9 and − 7 x . Therefore, it is not a monomial. It is a binomial.
Analyzing Option D Option D: 20 x 9 has only one term, and the exponent of the variable x is 9 , which is a non-negative integer. Therefore, this is a monomial.
Final Answer Therefore, the correct answer is D. 20 x 9
Examples
Monomials are fundamental in algebra and are used in various applications, such as calculating the area of a square ( x 2 ) or the volume of a cube ( x 3 ). Understanding monomials helps in simplifying complex algebraic expressions and solving equations. For instance, if you're calculating the revenue from selling a product at a fixed price per unit, the revenue can be represented as a monomial, where the price is the constant and the number of units sold is the variable.
