Polynomial Basic Concepts | Types of polynomials | Algebraic Expressions

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

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:

  1. a, b, c , x, y, z ….. are variables.
  2. 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
  • a2 + ab2 +25
  • x3 + 2x2 +10
  • 3x2 + 3xy + 4y2 + 15
  • 3xyz2 – 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: \sqrt{5} is also be a polynomial because it is a constant (= 2.2360…etc)

Ex – 3: \sqrt{y} 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:  \frac{5}{a +2}  is not a polynomial

Note: A polynomial never division by a variable

Ex-6 : \frac{5a+ 2b + a^2}{8}  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 : 3x3 + 3z2 – 10z + 0.5

The terms of above polynomial are 3x3, 3z2 , 10z , 0.5

The coefficient of 3x3 is 3

The coefficient of 3z2 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 8x0

The degree of polynomial is zero

Note:

  1. By adding or multiplying polynomials you get also a polynomial.
  2. 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 , \frac{5 a^2 + b}{4}  , x5

Here all algebraic expression containing one term

Binomial:

An algebraic expression containing two term is called a binomial

Ex ; 7 +x ,  8x2 +y, 8a2 + 2ab , 25a – b2 ,  . . . .  etc

Here all algebraic expression containing two terms

Trinomial:

An algebraic expression containing three term is called a trinomial

Ex ; y2 +x -7 ,  8x2 +y2+2xy, 8a2 + 2ab+25 , 25a2 – b2+ab ,  . . . .  etc

Here all algebraic expression containing three terms

Multinomials:

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

Ex ; y2+xy -x – 10 ,  8x2 +y2+2xy+x2y+12, 8a2 + 2ab+25 , 25a – b2+ab ,  . . . .  etc

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 , \sqrt{2} , 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: a2 + b, x + y2 + 9 , y2 + xy + 8 . . . .  etc

Cubic Polynomial

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

Ex: a3 + b, x3+ y2 + 9 , y3 + xy + 8 . . . .  etc

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: a4 + b3 + 2ab, x4 + y2 + 9 , 5y2 + x2y + 24 . . . .  etc

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

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Remainder and Factor Theorem Proof | Remainder and Factor Theorem Test

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Post Author: sivaalluri

My self Sivaramakrishna Alluri. Thank you for watching my blog friend

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

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