Question

What is the degree of the given monomial \[3\,mn\]?

Answer 1

Hint: We have to find the degree of the given monomial \[3mn\]. For this, we just have to add the powers of the variables involved in the term of the monomial of the polynomial expression. Here, \[3mn\] is a monomial in two variables \[m\] and \[n\]. So, addition of powers of the variables involved in the term of the monomial is the required result.

Complete step by step answer:
In this question, we have to find the degree of the given monomial \[3mn\].We can see that \[3mn\] is a monomial in two variables \[m\] and \[n\]. The given monomial here is \[3mn\]. We just have to add the powers of the variables involved in the term of the monomial of the polynomial expression. Here the monomial has two variables where the power of both \[m\] and \[n\] is \[1\]. So, the degree of monomial is \[\left( {1 + 1} \right)\] i.e., \[2\].

Therefore, the degree of the given monomial \[3mn\] is \[2\].

Additional information: The degree of monomial is defined as the sum of the exponents of the variables used in the monomial. In algebra, a monomial is an expression that contains only one term. In other words, a monomial is an expression that contains only one term. Generally, monomials include numbers, variables, or a number and a variable multiplied together, two or more variables multiplied together.

Note: A polynomial is an expression consisting of coefficients and variables which are also known as indeterminates. A monomial is an expression that does not contain any arithmetic operators. If in a given polynomial all the coefficients are equal to zero, then the degree of the zero polynomial is either set equal to \[ - 1\] or is undefined.