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 nonnegative 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
Ex6 : 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^{2} + 2ab , 25a – b^{2} , . . . . etc
Here all algebraic expression containing two terms
Trinomial:
An algebraic expression containing three term is called a trinomial
Ex ; y^{2} +x 7 , 8x^{2} +y^{2}+2xy, 8a^{2} + 2ab+25 , 25a^{2} – b^{2}+ab , . . . . etc
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^{2} +y^{2}+2xy+x^{2}y+12, 8a^{2} + 2ab+25 , 25a – b^{2}+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 , , 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^{2} + 9 , y^{2} + 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: a^{3} + b, x^{3}+ y^{2} + 9 , y^{3} + 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: a^{4} + b^{3} + 2ab, x^{4} + y^{2} + 9 , 5y^{2} + x^{2}y + 24 . . . . etc
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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