**Polynomial: **An algebraic expression is an expression which is made up of variables and constants along with some algebraic operations. The several parts of an algebraic expression seperated by + or – operations are called the terms of the expression. e.g.

(i) is an algebraic expression with three terms and three variables .

(ii) is an algebraic expression with three terms and two variables .

(iii) is an algebraic expression with two terms and one variable .

(iv) is an algebraic expression with one terms and one variable.

In an algebraic expression , if the powers of variables are non-negative integers , then it is a **polynomial.**

In the above examples , (i) and (ii) are polynomials, where as (iii) and (iv) are not polynomials.

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**Polynomials in one variable :**

Polynomials in one variable are algebraic expressions that consists of terms in the form of , where is non-negative integer and a is constant . e.g. all are polynomials in variable .

Each term of a polynomial has a coefficient . so in , the coefficient of is -1, coefficient of is and coefficient of is 3.

**Degree of a polynomial: **

The degree of a polynomial in a single variable is the highest power of in its expression. e.g. is a polyn0mial of degree 5 and is a polynomial of degree 6.

In general any polynomial of degree is an expression of the form

where are constants , and is a non-negative integer .

Here is called the constant term of the polynomial and are called the coefficient of respectively.

In particular if all the constants are zero , then we get **, ** the zero polynomial. Zero polynomial has no non-zero terms so the degree of zero polynomial is not defined.

**Constant polynomial: **

A polynomial containing only the constant term is called constant polynomial. e.g. all are constant polynomials.

Let is a non-zero constant polynomial ,

then can be written as

Therefore the degree of any non-zero constant polynomial is zero.

Based on the number of terms, polynomials are classified as

(i) A polynomial containing one term is called a **monomial**. e.g. etc. all are monomials.

(ii) A polynomial containing two terms is called a **binomial**. e.g. etc.

(iii)A polynomial containing three terms is called a **trinomial**. e.g. etc. all are trinomials.

**Linear polynomial : **

A polynomial of degree one is called a linear polynomial. A linear polynomial in is of the form

.

Any linear polynomials in have at most two terms . e.g. all are linear polynomials.

**Quadratic polynomial : **

A polynomial of degree 2 is called a quadratic polynomial. A quadratic polynomial in one variable will have at most tree terms. Any quadratic polynomial in will be of the form

e.g. all are quadratic polynomials.

###### **Cubic polynomial :**

** **A polynomial of degree 3 is called cubic polynomials. Any cubic polynomial can have at most 4 terms. all are examples of cubic polynomials.

Very good explanation & examples