Question

Which of the following is a monomial?
A. $3x$
B. $3x-4y$
C. $15+x$
D. $5xy+7$

Answer 1

Hint: We first characterise and classify the concept of polynomials. We break it based on the number of variables. We find the number of variables for the given options and the solution. If the number of total variables is 1 then it’s a monomial. Therefore, we can take $3x$ as monomial.

Complete step by step solution:
Polynomial mainly defines the expression with one or more variables with a particular order assigned to it. Terms can be in binary operations.
Based on the number of variables we can classify polynomials in monomial, binomial, trinomial and so on.
Monomial is the kind of polynomial which has only one variable.
From the given options only $3x$ has only one variable and that’s why it is a monomial.
All the other options $3x-4y$, $15+x$, $5xy+7$ have two variables x and y and that’s why they are not monomials. They are binomial.
The correct option is A.

Note: A monomial is an algebraic expression that has only one term. The basic building block of a polynomial is a monomial. A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent. The classification of polynomials is not dependent on the binary operation. Irrespective of the variables being in multiplication or addition, the count only determines the classification.