A monomial is a polynomial, which has only one term. As we know, the polynomials are the equations or algebraic expressions which consists of variables and coefficients and has one or more terms in it. Each term of the polynomial is a monomial. A polynomial involves the operation of addition, subtraction, multiplication, and non-negative integer exponents of variables.
A monomial is also a type of polynomial, like, binomial and trinomial, which is an algebraic expression having only a single term, which is a non-zero. Here in this article, we are going to learn more of monomial definition.
A monomial polynomial is the simplest form of a polynomial, as it consists of only a single term which makes it easy to do the operation of addition, subtraction and multiplication. It consists of either only one variable or one coefficient or product of a variable and a coefficient with exponents as whole numbers, which represent only one term, unlike binomial and trinomial, which consist of two and three terms respectively. A monomial cannot have a variable in the denominator.
Like, 4x is a monomial example, as it denotes a single term. In the same way, 23, 4x2, 5xy, etc.are examples of monomials but 23+x, 4xy, 5xy-2 are not monomials, as they don’t fulfill the monomial conditions.
We have learned in the introduction, that a monomial is a polynomial which consists of only one term. This is a very basic definition of a monomial. But let us learn the proper definition for monomial here with examples.
A monomial is a product of powers of variables with non- negative integer exponents, such that, if there is a single variable x, then the monomial is either a 1 or a power of xn of x, with n as positive integer and if for the product of multiple variables such that xyz, then the monomials can be given in the form of xaybzc where a,b,c are non-negative integers.
Now, in terms of the coefficient, the monomial is defined as the term with a non zero coefficient. The degree of a monomial is the sum of the exponents of all the included variables which forms monomials. For example, xyz2 have three degrees, 1,1 and 2. Therefore, the degree of xyz2 is 1+1+2 = 4.
Let us consider some of the variables and examples of monomials.
- p is a monomial with one variable and degree of the monomial is one.
- 5p2 is a monomial with 5 as coefficient and degree as two.
- p3q is a monomial with two variables and degree as 4(3+1).
- -6ty is a monomial of two variable t and y and a coefficient -6
- Let us consider x3+3x2+4x+12 is a polynomial, where x3,3x2,4x and 12 are the single terms and called as monomials.
Question Based on Monomials
Problem: Identify which of the following is a Monomial.
Answer: 3ab is a Monomial
Whereas 4b+c and 6x2+2y are binomials and a+b+c2 is a trinomial.
And all of these equations are called as a polynomial.
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