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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.