Standard Form of Polynomials - Examples and Videos - Teachoo

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Polynomials - Part 2

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Polynomials - Part 3 Polynomials - Part 4 Polynomials - Part 5 Polynomials - Part 6 Polynomials - Part 7 Polynomials - Part 8 Polynomials - Part 9 Polynomials - Part 10 Polynomials - Part 11

 

Equations of the type

x 3 − 3x 2 + 4x + 10

are called polynomials.

 

Here,

        x 3 , −3x 2 , 4x , 10 are called terms of polynomials.

 

A Polynomial has

  • Variables like x, y with powers as whole numbers (0, 1, 2, 3, ....). If Power is not a whole number , the equation is not a polynomial.
  • constants like 10

 

 

 

 

Polynomial in one variable

In this chapter,

We will be studying polynomials which are in one variable, i.e. only has x or y, but not both.

 

Example - x 2 + 2x - 3 is a polynomial in one variable as there is only x

But x 2 + 2y - 3x = 0 is not a polynomial in one variable as there is both x and y. 

 

Is x 2 + 24y + 1 a  polynomial in one variable?

-a-

Since there are two variables – x and y

It is not a polynomial in 1 variable

-ea-

 

Is y 4 – 10 a polynomial in one variable?

-a-

y 4 – 10 = y 4 – 10y 0

Here power are 4 and 0.

Since all powers are whole numbers, it is a polynomial

And since there is only one variable y,

It is a polynomial in one variable

-ea-

 

Is 5x -2 + 1 a polynomial in one variable?

-a-

Since power is -2

And -2 is not a whole number,

It is not a polynomial in one variable

-ea-

 

Is  3x 1/2 + 2 a polynomial in one variable?

-a-

Since power is 1/2

And 1/2 is not a whole number,

It is not a polynomial in one variable

-ea-

 

Is 3 a polynomial in one variable?

-a-

3 = 3x 0

Since power is 0

And 0 is a whole number,

It is a polynomial.

And since there is only 1 variable x,

It is a polynomial in one variable

-ea-

 

Note:

Constant numbers are also polynomials.

Example: 2, 3, 100, -988999 are all polynomials

  1. Chapter 2 Class 9 Polynomials (Term 2)
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.