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.

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.

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.

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:

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.