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Home >> Polynomials >>

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

 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 5x3 + 3x2 + x can be written as:
p(x) = 5x3 + 3x2 + x

Polynomial a3 + 2a + 3 can be written as:
q(a) = a3 + 2a + 3

Polynomial r2 + r + 35 can be written as:
f(r) = r2 + r + 35

A polynomial can have any number of terms.

Polynomials can be of following types:

• 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.

### 3x2 + 2x + 2

• Terms in given Polynomial are : 3x2 + 2x + 2

• Constant Term in given Polynomial is : 3x2 + 2x + 2

• Variables in given Polynomial are : 3x2 + 2x + 2

• Power / Exponent in given Polynomial is : 3x2 + 2x + 2

• Coefficients in given Polynomial are : 3x2 + 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 4y2 + 5x + 3
Solution : The given Polynomial is 4y2 + 5x + 3 so

Terms in given Polynomial are : 4y2 + 5x + 3

Constant Term in given Polynomial is : 4y2 + 5x + 3

Variables in given Polynomial are :4y2 + 5x + 3

Power in given Polynomial is : 4y2 + 5x + 3

Coefficient in given Polynomial are : 4y2 + 5x + 3

Example - 2 : Find terms, constant term, variables, power and coefficients from 5y2 + 6x - 4
Solution : The given Polynomial is 5y2 + 6x - 4 so

Terms in given Polynomial are : 5y2 + 6x - 4

Constant Term in given Polynomial is : 5y2 + 6x - 4

Variables in given Polynomial are : 5y2 + 6x - 4

Power in given Polynomial is : 5y2 + 6x - 4

Coefficient in given Polynomial are : 5y2 + 6x - 4

Example - 3 : Find terms, variables, power and coefficients from 5x3 + 4y2 + 3x
Solution : The given Polynomial is 5x3 + 4y2 + 3x so

Terms in given Polynomial are : 5x3 + 4y2 + 3x

Variables in given Polynomial are : 5x3 + 4y2 + 3x

Powers in given Polynomial are : 5x3 + 4y2 + 3x

Coefficients in given Polynomial are : 5x3 + 4y2 + 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