Polynomials are the algebraic expressions in which all the variables have exponents as whole numbers.

Let’s take an example, we have algebraic expression:

Above algebraic expression is polynomial because each variable ( and ) has exponent which is a whole number.

So, polynomials are made up of individual terms. In the example written above, we have polynomial

() consisting of 4 terms.

1^{st} term

2^{nd} term

3^{rd} term

4^{th} term

Each term has variable, coefficient and exponent associated with it.

For term , the variable is , coefficient is 1 and exponent is 2.

For term , the variable is , coefficient is 1 and exponent is 2

For term , the variable is , coefficient is 1 and exponent is 1.

For term , the variable is , coefficient is -4 and exponent is 3.

**Can you write few examples of polynomials?**

(i)

(ii)

(iii) 3 (It is polynomial because it can be written as , it is also called constant polynomial.)

(iv)

(v)

(vi)

(vii)

(viii)

**Can you write few algebraic expressions which are not polynomials?**

(i) (Exponent of variable is not a whole number)

(ii) (Exponent of variable is not a whole number)

(iii) (Exponent of variable is not a whole number)

(iv) (Exponent of variable is not a whole number)

(v) (Exponent of variable is which is not a whole number)

**At this point, you should be able to answer correctly if the given algebraic expression is polynomial or not.**

It is good to know that polynomials consisting of just a single term are called monomials. For example : and are all monomials.

Polynomial consisting of two terms is called binomial. For example: and are examples of binomials.

Polynomials consisting of three terms are called trinomials. For example:

and are examples of trinomials.

0 is also a polynomial called zero polynomial. We get zero polynomial if all the coefficients are equal to zero.

In the next article, we will be discussing about the degree of polynomials.