## DEFINITION:

A polynomial is an algebraic expression in which the denominator do not have variables and all the variables that appear will be powers of positive integer.

**For Example:**

The trinomial -2xy-1+3x-4 is not a polynomial but however the trinomial 3x2y2+4xy-2 is a polynomial in the variables x and y.

The term -2 is called the constant term of the polynomial. The numerical coefficients in a polynomial is called the coefficients of the polynomial.

## THE DEGREE OF THE POLYNOMIAL:

Degree of the polynomial is obtained by summing up the exponents of all the variables in that term and more important is one should consider a variable with no exponent as being power 1.

**For Example:**

In the polynomial 6x2y3-7y2z4x+5z-2

the term 6x2y3 has degree 2+3=5

the term -7y2z4x has degree 2+4+1=7

the term 5z has degree 1

the constant term is of degree 0 x

The degree of the highest degree term with non zero coefficient in a polynomial is called the degree of the polynomial.

## POLYNOMIALS IN ONE VARIABLE:

P(x)= anxn+an-1xn-1+…………..+a2x2+a1x+a0 , an0.

Where a0 ,a1, a2, …….an-1, an are constants and n is a non negative integer. n is the degree of the polynomial.

a1, a2, a3, …………,an-1, an are coefficients of x, x2, x3,………….,xn-1, xn respectively.

a0 is the constant term.

anxn, an-1xn-1, ………….,a2x2, a1x, a0 are the terms of the polynomial.

**For Example:**

In the polynomial 8z2+5z-1 the coefficient of z2 is 8, the coefficient of z is 5 and -1 is the constant term.

The three terms of the polynomial are 8z2, 5z and -1.

## TYPES OF POLYNOMIAL BASED ON THE NO. OF TERMS:

### MONOMIAL:

The polynomial which has only one term is called monomial.

Example: 8x

### BINOMIAL:

The polynomial which has only two terms is called binomial.

Example: 7y+z

### TRINOMIAL:

The polynomial which has only three terms is called trinomial.

Example: 4a+3b+2c

## TYPES OF POLYNOMIAL BASED ON DEGREE:

**CONSTANT POLYNOMIAL:**

A polynomial which has degree to be zero is called constant polynomial.

General Form: P(x)= r, where r is a real number

Example: P(x)= 5

**LINEAR POLYNOMIAL:**

A polynomial which has degree to be one is called linear polynomial.

General Form: P(x)= px+q, where p and q are real numbers, p0.

Example: P(x)=y+3

**QUADRATIC POLYNOMIAL:**

A polynomial which has degree to be two is called quadratic polynomial.

General Form: P(x)= px2+qx+r, where p,q and r are real numbers, p0.

Example: P(x)= 5x2+4x+5

**CUBIC POLYNOMIAL:**

A polynomial which has degree to be three is called cubic polynomial.

General Form: P(x)= px3+qx2+rx+s, where p,q,r and s are real numbers, p0.

Example: P(x)= 4x3-1