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: 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 : 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:
- 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 , , 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 , , 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
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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