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

Table of Contents

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 has only one term, so it can be called a polynomial

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

Ex – 3: √y is not a polynomial because the exponent of the 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 be divided by a constant but never division by a variable

Degree of polynomial:

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

The degree of a term is the sum of the exponents of its variable factors, and the degree of the 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 the constant number 8 and it can be written as 8x⁰

The degree of a polynomial is zero

Note:

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