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# CBSE Class 9 Chapter 2 : Polynomials

## CBSE Class 9 Chapter : 2.1

## What is a constant ?

In algebra, constant is a number or a letter which has a fixed value.

## What is a variable ?

In algebra, a variable is a letter which do not have fixed value. Its value can vary from expression to expression.

For Example : In this expression C and r are variables, but 2 and are constants. Because the value of 2 and are known to us and same for all cases, but the value of **C** will change when the value of **r** will change. Smaller the radius smaller the circumference, larger the radius larger the circumference but value 2 and are fixed for smaller radius as well as larger radius.

## What is an algebraic expression ?

In mathematics an algebraic expression can be defined as a combination of integer constants, variables and algebraic operations like addition, subtraction, multiplication, division and exponentiation by a rational exponent.

For example

## What is a term in algebraic expression ?

A term in an algebraic expression can be defined as a combination of integer constants, variables and algebraic operations like multiplication, division and exponentiation by a rational exponent. (Note that we can not use addition and subtraction. Addition and subtraction separates one term from another.)

Example :

## What is a coefficient ?

A coefficient can be defined as a multiplicative factor in a term of any expression.

Example :

- : 3 times x so 3 is the coefficient of x.
- : 1 time , so 1 is the coefficient of x.
- : In this example if asked what is the coefficient of x ? we can say here x is present 0 times, so coefficient of x in this term is 0.

## What is a Polynomial ?

In mathematics a polynomial can be defined as a combination of integer constants, variables and algebraic operations like addition, subtraction, multiplication, division and exponentiation by a whole number exponent.

For Example

- is a polynomial in one variable
- is a polynomial in one variable
- is a polynomial in two variables
- is a polynomial in two variables

## What is a constant polynomial ?

When in a polynomial only constants are present, it is called a constant polynomial.

## What is a zero polynomial ?

When in a polynomial only one term zero is present, it is called a zero polynomial.

## What is a monomial ?

A polynomial having only one term is known as a monomial.

## What is a binomial ?

A polynomial having only two terms is known as a binomial.

## What is a trinomial ?

A polynomial having three terms is known as a trinomial.

## What is the degree of a term ?

The degree of a term can be defined as the sum of the exponents of the variables appear in it.

## What is the degree of a polynomial ?

The highest degree of the individual terms(with non-zero coefficients) of the polynomial is treated as the degree of the polynomial. The degree of constant polynomial is zero and zero polynomial is not defined.

## What is a linear polynomial ?

A polynomial with degree one is called a linear polynomial.

## What is a quadratic polynomial ?

A polynomial with degree two is called a quadratic polynomial.

## What is a cubic polynomial ?

A polynomial with degree three is called a cubic polynomial.

## CBSE Class 9 Chapter : 2.2

## What is a root or zero of a polynomial ?

A root or zero of a polynomial is the value of variable for which the polynomial becomes a zero polynomial. Or we can say can be the root or zero of polynomial if .

Example :

**1** is the root or zero of polynomial **x-1** because, if we put the value of **x** as **1** in the polynomial (**x-1**) then it becomes a zero polynomial.

Remember : A non-zero constant polynomial has no zeros. A Polynomial can have more then one zeros.

## CBSE Class 9 Chapter : 2.3

## Remainder Theorem

We know that Dividend = (Divisor X Quotient) + Remainder or .

Remainder theorem or Little Bezout’s theorem is an approach of Euclidean division of polynomials. According to remainder theorem if we divide any polynomial of degree greater then or equal to one by a linear polynomial , we will get a smaller polynomial along with a remainder. and this remainder obtained is equal to the value obtained by .

In other words we can say will be completely divisible by if and only if .

## CBSE Class 9 Chapter : 2.4

## Factor Theorem

If we present remainder theorem in other words it becomes factor theorem. Factor theorem says if is any polynomial of degree greater then or equal to one and where a is any real number, then is definitely a factor of .

## Factorising a quadratic polynomial by splitting the middle term.

Let be any quadratic polynomial. To factorise it by splitting the middle term, we have to split the middle term into such that, .

## CBSE Class 9 Chapter : 2.5

## Algebraic identities

We can also use some algebraic identities to factorise the algebraic expressions.

If you like this consider enrolling : CBSE Class 9th Mathematics Made Easy

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