In this article brief about basic *concepts of Polynomial *Expressions. *Polynomial definition, examples of polynomials, Degree of polynomials, types of polynomials according to its terms and according to degree*

## Polynomial Definition | Degree of a Polynomial | Types of Polynomials

Contents

In algebra, we deal with two types of symbols namely **constants** and **variables**

**Constants –** A symbol having a fixed numerical is called a constant.

*Example:* 5, -8, 5/6, . . . . etc

**Variables –** A symbol which takes various numerical values a variable

*Example:*

- a, b, c , x, y, z ….. are variables.
- We know that the perimeter of the circle of radius “ r” is given by P = 2πr. Here “2” and ”π” are constants and r and P are variables

### Polynomial definition

A combination of constants and variables, connected by ‘ + , – , x & ÷ (addition, subtraction, multiplication and division) is known as an **algebraic expression.**

An algebraic expression in which the variables involves have only non-negative integral powers, is called** polynomial**

#### Examples for polynomials:

- x
- 20
- x – 5
- a
^{2}+ ab^{2}+25 - x
^{3}+ 2x^{2}+10 - 3x
^{2}+ 3xy + 4y^{2}+ 15 - 3xyz
^{2}– 3x + 10z + 0.5

**How to find the polynomial**

**Ex – 1: 20**

Here “20” is just a constant and also having only one term, so it can be called as** polynomial**

**Ex – 2: **is also be a polynomial because it is a constant (= 2.2360…etc)

**Ex – 3:** is not a polynomial because the exponent of variable is “½”

**Note: **Exponents of variables in a polynomial allowed only 0, 1, 2, 3, … etc

**Ex – 4: 4a ^{-5}** is not a polynomial because the exponent is “-5”

**Ex – 5: ** is not a polynomial

**Note**: A polynomial never division by a variable

**Ex-6 :** is a polynomial

**Note: ***A polynomial can divide by a constant but never division by a variable*

### Degree of polynomial:

In a polynomial the largest exponent value of any given variable, that value is *degree of that polynomial*.

Degree of a term is the sum of the exponents of its variable factors and *degree of polynomial* is the largest degree of its variable term.

Ex – 1 : **3x ^{3} + 3z^{2} – 10z + 0.5**

The terms of above polynomial are **3x ^{3}, 3z^{2} , 10z , 0.5 **

The coefficient of 3x** ^{3}** is 3

The coefficient of 3z** ^{2}** is 2

The coefficient of -10z is 1

**The Degree of the above polynomial is 3**** **

Ex – 2 : **8**

In the above example contains constant number 8 and it can be written as **8x ^{0}**

The *degree of polynomial* is** zero**

**Note:**

- By adding or multiplying polynomials you get also a polynomial.
- While writing a polynomial in a standard form, put the terms with the highest degree first.

**Types of polynomials according to number of terms (Algebraic expressions)**

**Monomial**

An algebraic expression containing only one term is called a *monomial*

**Ex** ; 7, 8x , , x^{5}

Here all algebraic expression containing one term

#### Binomial:

An algebraic expression containing two term is called a *binomial*

**Ex** ; 7 +x , 8x** ^{2}** +y, 8a

**+ 2ab , 25a – b**

^{2}**, . . . . etc**

^{2}Here all algebraic expression containing two terms

#### Trinomial:

An algebraic expression containing three term is called a *trinomial*

**Ex ;** y** ^{2}** +x -7 , 8x

**+y**

^{2}**+2xy, 8a**

^{2}**+ 2ab+25 , 25a**

^{2}**– b**

^{2}**+ab , . . . . etc**

^{2}Here all algebraic expression containing three terms

#### Multinomials:

An algebraic expression containing more than three term is called a *multinomials*

**Ex ;** y** ^{2}**+xy -x – 10 , 8x

**+y**

^{2}**+2xy+x**

^{2}**y+12, 8a**

^{2}**+ 2ab+25 , 25a – b**

^{2}**+ab , . . . . etc**

^{2}Here all algebraic expression containing more than three terms

### Types of polynomials according to degree

#### Constant Polynomials

A polynomials having one term consisting of a constant only is called a *constant polynomials*

**Ex ;** 8 , , 35 , . . . etc

#### Liner Polynomial

In a polynomial the largest exponent value of any variable is one then it is called *liner polynomial*

**Ex**: a + b, x + 25 , y + x + 25 . . . . etc

#### Quadratic Polynomial

In a polynomial the largest exponent value of any given variable is two then it is called Quadratic polynomial

**Ex:** a** ^{2}** + b, x + y

**+ 9 , y**

^{2}**+ xy + 8 . . . . etc**

^{2}#### Cubic Polynomial

In a polynomial the largest exponent value of any given variable is two then it is called Quadratic polynomial

**Ex**: a** ^{3}** + b, x

**+ y**

^{3}**+ 9 , y**

^{2}**+ xy + 8 . . . . etc**

^{3}#### Bi quadratic polynomial or Quartic polynomial

In a polynomial the largest exponent value of any given variable is four then it is called* Quartic polynomial*

**Ex**: a** ^{4}** + b

**+ 2ab, x**

^{3}**+ y**

^{4}**+ 9 , 5y**

^{2}**+ x**

^{2}**y + 24 . . . . etc**

^{2}I Hope you liked this article about** basic knowledge of polynomial functions**;. Give feed back, comments and please don’t forget to share it.

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## 2 thoughts on “Polynomial Basic Concepts | Types of polynomials | Algebraic Expressions”

## Confidence Dennis Dzaka

(November 28, 2018 - 6:12 pm)Many thanks for this educative lesson. Keep them coming, Sir!

## sivaalluri

(November 30, 2018 - 5:04 pm)Thank you Confidence Dennis Dzaka