Algebra Maths

Polynomials

polynomials
Written by Mary Christina

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 , an\ne0.

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

About the author

Mary Christina

Mary Christina from Chennai, India. She has completed Master Degree in Mathematics and she loves to teach and share about her knowledge in maths for High School and College Students...