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What Is a Monomial?

In algebra, a monomial is an expression that has a single term, with variables and a coefficient. In this guide, you will learn more about the definition of a monomial and its factoring.

What Is a Monomial?

Monomials are the building blocks of polynomials and are called terms when they are part of larger polynomials. In other words, each term in a polynomial is a monomial.

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A step-by-step guide to monomial

A monomial is defined as a phrase that has a single non-zero term. It consists of different parts such as variables, coefficients, and degrees. The variables in a monomial are the letters in it.

Coefficients are numbers that are multiplied by the variables of the monomial. The degree of a monomial is the sum of the exponents of all the variables. 

How to find a monomial?

A monomial can be easily identified with the help of the following properties:

  • A monomial expression must have a single non-zero term.
  • The exponents of the variables must be non-negative integers.
  • There should not be any variable in the denominator.

How to find a degree of a monomial?

The degree of a monomial is the sum of the exponents of all the variables. It is always a non-negative integer. For example, the degree of the monomial abc2 is 4. The exponent of the variable a is 1, the exponent of variable b is 1, and the exponent of variable c is 2. Adding all these exponents, we get, 1+1+2=4.

How to Factor Monomials?

When factoring monomials, we always factor in coefficients and variables separately. Factoring a monomial is as simple as factoring a whole number.

In the same way, we can factorize a monomial. We just have to remember that we always factorize coefficients and variables separately.

Example: Factorize the monomial, 15y3.

Solution:

In the given monomial, 15 is the coefficient, and y3 is the variable.

  • The prime factors of the coefficient,15, are 3 and 5.
  • The variable y3 can be factored in as y×y×y.
  • Therefore, the complete factorization of the monomial is 15y3=3×5×y×y×y.

Monomial – Example 1:

 Is 14zx a monomial expression?

Solution:

The expression has a single non-zero term, but the denominator of the expression is variable. Therefore, the expression 14zx is not a monomial.

Exercises for Monomial

Factor each of the following monomials.

  1. 10x2
  2. 8x2y2
  3. 18xy
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  1. 2.5.x.x
  2. 2.2.2.x.x.y.y
  3. 2.3.3.x.y

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