Classification of Polynomials

Polynomial is being categorized according to the number of terms and the degree present. Polynomial equations are the equation that contains monomial, binomial, trinomial and also the higher order polynomial. The form of a monomial is an expression is  where n is a non-negative integer. The variable ‘a’ is called as the coefficient of and n is the degree of the monomial. Based on the value, one term is called as monomial (when n = 1), two-degree polynomial (when n = 2) and three-degree polynomial (when n = 3).

Example: The polynomial is classified by the number of terms as:

1. Monomial – One term – 3x
2. Binomial – Two Term – 7a-5
3. Trinomial – Three Term – 

Types of Polynomials

1. Monomial = The polynomial with only one term is called monomial. A number or a product of a number and a variable. Example: -2x,,are monomials.
2. Binomial = The polynomial with two-term is called binomial. Two monomials are connected by + or -. Example: ,are binomials.
3. Trinomial = The polynomial with three-term are called trinomial. Three monomials are connected by + or -. Example:  are trinomials.
4. Constant Polynomial: The polynomial containing only the constant term is a constant polynomial. Example: 45,-78 are constant polynomial.
5. Polynomial: If the expression contains more than three terms, then the expression is called a Polynomial. More than three monomials connected by + or -. Example:  is a polynomial.

Example: Identify the types of polynomials:

1. 
2. 
3. 
4. 
5. 
6. -89

Solution: 1. Monomial, 2. Trinomial, 3. Binomial, 4. Monomial, 5. Polynomial, 6. Constant.

Degree of Polynomials

The highest value of the exponent in the expression is known as Degree of Polynomial. The degree of a polynomial is the largest exponent. It is also known as an order of the polynomial. While finding the degree of the polynomial, the polynomial powers of the variables should be either in ascending or descending order.

1. Linear Polynomial: If the expression is of degree one then it is called a linear polynomial. For Example 5x+2,50z+3.
2. Quadratic Polynomial: If the expression is of degree two then it is called a quadratic polynomial.For Example .
3. Cubic Polynomial: If the expression is of degree three then it is called a cubic polynomial.For Example .

Example: Classify these polynomials by their degree:

1. 
2. 
3. 
4. 

Solution: 1. 3rd Degree, 2. 1st Degree, 3. 5th Degree, 4. 2nd Degree.

Exercise

Identify the types of polynomials:

1. 
2. 
3. 10pqr
4. 
5. 
6. -59

Classify these polynomials by their degree:

1. 
2. 
3. 
4. 
5.