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## Polynomials can have Coefficients, Terms, Variables and involves Powers of the Variable

Zero Polynomial

Monomial

Binomial

Trinomial

(You can study these types from the above provided link)

Have a look at the below expression and study what are terms, constant term, variables, power and coefficients of Polynomial.

### 3x^{2} + 2x + 2

** Terms in given Polynomial are : ** 3x^{2} + 2x + 2

** Constant Term in given Polynomial is : ** 3x^{2} + 2x + 2

** Variables in given Polynomial are : ** 3x^{2} + 2x + 2

** Power / Exponent in given Polynomial is : ** 3x^{2} + 2x + 2

** Coefficients in given Polynomial are : ** 3x^{2} + 2x + 2

Note: If Power or Exponent is negative then it is not a polynomial . For example x^{-2} or 2x^{-2}

Let's study few examples and find terms, constant term, variables, power and coefficients of Polynomial

** Example - 1 : Find terms, constant term, variables, power and coefficients from 4y**^{2} + 5x + 3

Solution : The given Polynomial is 4y^{2} + 5x + 3 so

Terms in given Polynomial are : 4y^{2} + 5x + 3

Constant Term in given Polynomial is : 4y^{2} + 5x + 3

Variables in given Polynomial are :4y^{2} + 5x + 3

Power in given Polynomial is : 4y^{2} + 5x + 3

Coefficient in given Polynomial are : 4y^{2} + 5x + 3

** Example - 2 : Find terms, constant term, variables, power and coefficients from 5y**^{2} + 6x - 4

Solution : The given Polynomial is 5y^{2} + 6x - 4 so

Terms in given Polynomial are : 5y^{2} + 6x - 4

Constant Term in given Polynomial is : 5y^{2} + 6x - 4

Variables in given Polynomial are : 5y^{2} + 6x - 4

Power in given Polynomial is : 5y^{2} + 6x - 4

Coefficient in given Polynomial are : 5y^{2} + 6x - 4

** Example - 3 : Find terms, variables, power and coefficients from 5x**^{3} + 4y^{2} + 3x

Solution : The given Polynomial is 5x^{3} + 4y^{2} + 3x so

Terms in given Polynomial are : 5x^{3} + 4y^{2} + 3x

Variables in given Polynomial are : 5x^{3} + 4y^{2} + 3x

Powers in given Polynomial are : 5x^{3} + 4y^{2} + 3x

Coefficients in given Polynomial are : 5x^{3} + 4y^{2} + 3x

** Example - 4 : Is 25 a polynomial **

Solution - Yes 25 is a polynomial as one term is allowed in polynomial and this 25 is also a constant

** Example - 5 : Is x**^{-3} is polynomial

Solution : No, x^{-3} is not a polynomial because its power is negative

### Study More Solved Questions / Examples

Ordering of Polynomials Types of Polynomials Addition of Polynomials Subtraction of Polynomials Multiplication of Polynomials Division of Polynomials Types of Degree / Powers in Polynomials Difference between Polynomials of Integers & Rationals Factoring of Quadratic Polynomials Find Value of Polynomial Find Zero of Polynomial Remainder Theorem in Polynomial

Before you understand this topic you should read -

What is Algebraic Expression ?

What are Terms ?

An algebraic Expression with one or more terms is called ** Polynomials **.

Eg. 2a, 5x + y, 2x2 + 3x + y, all are polynomials

If the variable in the polynomial is x, we may denote the polynomial by p(x) or q(x) or r(x)… etc

For example:

Polynomial 5x^{3} + 3x^{2} + x can be written as:

p(x) = 5x^{3} + 3x^{2} + x

Polynomial a^{3} + 2a + 3 can be written as:

q(a) = a^{3} + 2a + 3

Polynomial r^{2} + r + 35 can be written as:

f(r) = r^{2} + r + 35

A polynomial can have any number of terms.

** Polynomials can be of following types: **

(You can study these types from the above provided link)

Have a look at the below expression and study what are terms, constant term, variables, power and coefficients of Polynomial.

Note: If Power or Exponent is negative then it is not a polynomial . For example x

Let's study few examples and find terms, constant term, variables, power and coefficients of Polynomial

Solution : The given Polynomial is 4y

Terms in given Polynomial are : 4y

Constant Term in given Polynomial is : 4y

Variables in given Polynomial are :4y

Power in given Polynomial is : 4y

Coefficient in given Polynomial are : 4y

Solution : The given Polynomial is 5y

Terms in given Polynomial are : 5y

Constant Term in given Polynomial is : 5y

Variables in given Polynomial are : 5y

Power in given Polynomial is : 5y

Coefficient in given Polynomial are : 5y

Solution : The given Polynomial is 5x

Terms in given Polynomial are : 5x

Variables in given Polynomial are : 5x

Powers in given Polynomial are : 5x

Coefficients in given Polynomial are : 5x

Solution - Yes 25 is a polynomial as one term is allowed in polynomial and this 25 is also a constant

Solution : No, x