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Types of Polynomials

Based on the number of terms of the given polynomial, it can be divided into monomial, binomial, trinomial, constant polynomials.

 

Monomial

The polynomial with only one term is called monomial.

 

Example : -5x,, etc., are monomials.

 

Binomial

The polynomial with two terms is called binomial.

 

Example :   p(x) =

 

q(x) =

r(x

) = are binomials.

 

Trinomial

The polynomial with three terms are called trinomial.

 

Example :

 s(x) =

P(x) = are trinomials.

 

Constant polynomial

Polynomial containing only constant terms is a Constant polynomial.

 

Example : -45, 56, -98 are constant polynomials.

 

Polynomial

If the expression contains more three terms, then the expression is called a Polynomial.

 

Example :  is a polynomial

 

Table: Polynomials classified according to their terms:

Number of terms

Example

Name

1

0

Zero Polynomial

1

Monomial

2

Binomial

3

Trinomial


Monomial: A number or a product of a number and a variable

Binomial: Two monomials connected by + or -.

Trinomial: Three monomials connected by + or -.

Polynomial: More than three monomials connected by + or -.

Degree of the Polynomial

The highest power of the polynomial is called the degree of the polynomial. Degree of the polynomial is also called the 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.

 

Example : consider the polynomial,

Here the polynomial is arranged in descending order, the degree of the polynomial is 4.

 

Linear Polynomial : If the polynomial is of degree one then it is called a Linear Polynomial.
 

Example :

are linear polynomials.

Quadratic Polynomial: If the degree of the polynomial is two then it is called a Quadratic polynomial.

 

Example :  are Quadratic polynomial.

Cubic Polynomial: If the degree the polynomial is three then it is called a Cubic polynomial.

 

Example : are Cubic polynomials.

 

Table : Polynomial Classified according to their degree

 

Degree of polynomial

Example

Name of polynomial

undefined

0

Zero

0

1

(non-zero) constant

1

Linear

2

Quadratic

3

Cubic

4

Quartic or biquadratic

5

Quintic

6

Sextic or hexic

7

Septic or heptic

8

Octic

9

Nonic

10

Decic





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