In algebra, we have seen that, polynomial is the higher degree equation with number of terms in two or more variables with coefficients.
The each term present in the polynomial which includes variable, coefficient and some exponent also is called as the monomial. Hence, we can say that monomials are the base of polynomials.
Mono means single i.e. a single non-zero term with variable, coefficient and positive non-zero degree is the monomial.
Note: The degree of the monomial is the sum of powers of variables in it. And the degree of monomial must be non-zero whole number always.
Consider the example 5x2y,is the monomial since it has only one non-zero term with variables x and y and also the coefficient which is 5.
And here, the degree of monomial is 3 = power of x + power of y = 2 + 3.
To understand more clearly we see following examples.
The above is the single non-zero term with variables x and y, the coefficient is 6 and the degree of monomial is (1 + 2) = 3, hence it is the monomial.
The above is the single non-zero term with variable x, coefficient is 7/4 and the degree is 1. Hence, it is the monomial.
3) 4xy2 + 2xy
The above is not the single terms, the above equation has two terms and hence it is not the monomial.
The above is the single non-zero term with two variables x and y, with coefficient 5.
But, it is not the monomial as the degree of monomial is not a whole number.
Since degree of monomial = 1+2/3 = 5/3 and 5/3 is not the whole number.
The above is the single non-zero term with variables x and y, with coefficient 8.
But the degree of the term is not a whole number, it is a variable y.
Hence, it is not the monomial.
The above is the single non-zero term with variables x and y, with coefficient 9.
But here the denominator of the term is in variable which is x.
And hence, it is not the monomial.
- Thus, monomial is the single non-zero term in the form of variables with coefficients, and the degree of monomial is the positive whole number.
- Similarly, if there are two single non-zero terms i.e. two monomials are present in a equation then it is the binomial.
2x + 3y is the binomial as it contains two monomials.
- Similarly, if there are three monomials in a equation, then it is the trinomial.
ax2 + bx +c, is the trinomial as it contains three terms.