Monomials, Binomials, Trinomials and Polynomials

In mathematics, monomials, binomials, trinomials and polynomials are all algebraic expressions. The expressions that are represented using unknown variables, constants and coefficients, are called algebraic expressions. A variable can take any value, it is not fixed but a constant is a fixed value.

To make these algebraic expressions such as monomials, binomials, trinomials and polynomials, we combine the variables and constants using arithmetic operations (+, -, x, ÷). For example, 3x+2 is an expression, which has two parts 3x and 2, separated by the ‘+’ sign. These two parts are called terms here.

What are Terms?

The parts of algebraic expressions that are separated by addition or subtraction, are called terms. The number of terms decides the type of expression, whether it is a monomial, binomial, trinomial or polynomial.

These terms are made of a product of variables and coefficients that are added together to form expressions. For example, 2x and 9 are added together to form the expression: 2x + 9.

Note: A single constant value can also be a term. It is not necessary that a term is a combined form of both variable and constant. In the expression, 3 + 4x, 3 is also a term.

Also, read: Like and Unlike Algebraic Terms

Factors of Terms

The factors are the value that divides the original value evenly. Thus, the factors of terms are the variables or constants that collectively make the term.

For example, if 4xy is a term, then the factors of 4xy are 4, x and y.

Factors containing variables are said to be algebraic factors.

What is a Monomial?

A monomial is an algebraic expression that has only one term.

Or we say single term expression is a monomial.

The examples of monomials are:

  • 12x
  • 12
  • -25x
  • 24y
  • 4a
  • 4b
  • xy

What is a Binomial?

A binomial is an algebraic expression that has two unlike terms.

Facts:

  • Like terms have the same algebraic factors but unlike terms have different algebraic factors.
  • 3x and 4x are like terms whereas 3x and 4y are unlike terms

The examples of binomials are:

  • x + y
  • m – 5
  • mn + 4m
  • a2 – b2
  • xy + 5
  • 4m – 7n
  • 3p – 2q

What is a Trinomial?

A trinomial is an algebraic expression that has three terms in it.

The examples of trinomials are:

  • x + y + 7
  • ab + a +b
  • 3x 2 – 5x + 2
  • m + n + 10

The expression x + y + 3x is not a trinomial as the terms x and 3x are like terms.

What is a Polynomial?

The term poly means many. An expression that has more than one term is called polynomial, non-negative integral exponents of a variable.

Examples of polynomial expression include:

  • ax + by + ca
  • x3 + 2x + 3
  • 1.2 ab – 2.4 b + 3.6 a
  • 1 + x2 + xy

Degree of a polynomial

The greatest power or exponent of a polynomial is called its degree.

For example, the degree of x3 +x2+x is 3.

Also, check: Degree of a Polynomial

Solved Examples

Q.1 Which of the following are monomials, binomials and trinomials?

  • 4y – 7z
  • ab – a – b
  • y2
  • 100x
  • aX+by+cz
  • X2 + y2
  • 7mn
  • 5-3t

Solution: The respective monomials, binomials and trinomials are:

Monomials

Binomials

Trinomials

  • y2
  • 100x
  • 7mn
  • 4y – 7z
  • X2 + y2
  • 5-3t
  • ab – a – b
  • aX+by+cz

Q.2: Add 4x + 3y and x + z.

Solution: Given two binomials, 4x + 3y and x + z.

Adding the given expressions we get;

⇒ (4x + 3y) + (x + z)

⇒ 4x + 3y + x + z

There are two similar terms that can be added. Thus, we get;

⇒ 4x + x + 3y + z

⇒ 5x + 3y + z

Hence, is the answer.

Practice Questions

  • Give four examples of monomials.
  • Give four examples of binomials.
  • Give four examples of trinomials.

Frequently Asked Questions – FAQs

What is the difference between monomials, binomials, trinomials and polynomials?

A monomial has a single term, a binomial has two terms, a trinomial has three terms and a polynomial has one or more than one term.

What are the examples of monomial, binomial and trinomial?

The example of a monomial, binomial and trinomial are 3mn, 3mn + x and 3mn + x – y, respectively.

What is the difference between a monomial and a polynomial?

A monomial is also a type of polynomial. But a polynomial is not always a monomial.

Is 5x + 8x a monomial?

5x + 8x is a monomial because 5x and 8x are like terms and can be added.
5x + 8x = 13x

What are the factors of a monomial, 9xyz?

The factors of monomial 9xyz are 9, x, y and z.

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