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Monomials, Binomials, Trinomials, and Polynomials are all mathematical algebraic expressions. We combine the variables and constants using different arithmetic operations (+, -, x, ÷) to make these algebraic expressions.
For example, 8x+9 is an expression that has two parts, 8x and 9, separated by the ‘+’ sign. These two parts are called terms here.
Polynomials
Polynomials are defined as the type of algebraic expressions whose variables have only non-negative integers as their powers.
For example:
f(x) = 8x² – 5x + 13 is a polynomial.
What are Terms?
The parts of algebraic expressions that are separated by different arithmetic operations 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 combined with mathematical operations to form expressions. For example, 2x and 9 are added together to form the expression: 2x + 9.
Note: A single constant value is a term as well. A term doesn’t need to be a combination of both a variable and a constant. In the expression 3 + 4x, 3 is also a term.
Factors of Terms
The factors of the terms are defined as the variables or constants separately that combine to form the original term.
For example, if 4xy is a term, then the factors of 4xy are 4, x, and y.
Algebraic factors are defined as the factors containing variables.
Types of Polynomials
As previously mentioned, the polynomials can be classified in two ways:
- On the basis of the degree
- On the basis of the number of terms.
- The types of polynomials on the basis of degree are zero polynomial, linear, quadratic, and cubic polynomials.
- The types of polynomials on the basis of the number of terms: monomials, binomials, trinomials, etc.
Types of Polynomials on the Basis of the Number of Terms
Depending upon the number of terms, types of polynomials are divided into the following categories:
- Monomial
- Binomial
- Trinomial
- Polynomial containing 4 terms (Quadrinomial)
- Polynomials containing 5 terms and so on …
These polynomials can be combined using either of the arithmetic operations.
A few examples of Non-Polynomials are: 1/x+2, 1/x³
Monomial
A monomial is a Polynomial expression that contains only one term.
To make a monomial expression, the single term should be a non-zero term.
A few examples of monomials are:
5x, 3, 6a⁴, -3xy
Binomial
A binomial is a polynomial expression that contains exactly two terms.
A binomial can be considered as a sum or difference between two or more monomials. A few examples of binomials are:
– 5x+3,
6a⁴ + 17x
x³+xy
Trinomial
A trinomial is an expression that is composed of exactly three terms. A few examples of trinomial expressions are:
7a⁴+2x+7
4x² + 9x + 7
Polynomial
A polynomial is an expression that is composed of one or more than one term. A few examples of Polynomial expressions are:
7x²+2xy+7y²+8
4x³ + 9x² + 7x + 10xy + 15
Polynomial containing exactly 4 terms is sometimes referred to as Quadrinomial.
Comparison between Monomial, Binomials, Trinomials, and Polynomials
| Monomial | Binomial | Trinomial | Polynomials |
| One term | Two-term | Three-term | 1 or more than 1 term |
| x y² |
x⁵+y² m⁴-n² |
x²-y³+z⁴ p²+q²+pq |
x²+y²+z²+xyz p²+q²+pq+p²q+q²p |
FAQs on Monomial, Binomials, Trinomials, and Polynomials
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? Ans. The example of a monomial, binomial, and trinomial are 7mn, 7mn + m², and 7mn + m² – n², respectively.
The example of a monomial, binomial, and trinomial are 7mn, 7mn + m², and 7mn + m² – n², respectively.
What is the difference between a monomial and a polynomial?
A monomial is a type of polynomial that has exactly 1 term. But a polynomial is not always a monomial. It can be any expression with one or More than one term.
Is 9x + x a monomial?
9x + x is a monomial because 9x and x are like terms and can be added. 9x + x = 10x
What are the factors of the given monomial expression, 18xyz?
The factors of monomial 18xyz are 18, x, y, and z.
