Introduction

Chapter 2 Class 10 Polynomials
Concept wise

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

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.