SUBMITTED TO:- SUBMITTED BY:- VINOD PATIL KRISHNA GUPTA

SAMYAK JAIN PRADHUM PATHAK

Class:- 10th B

SESSION: 2013-2014

Subject :-Mathematics

WHAT IS A POLYNOMIALA polynomial is an expression made

with constants, variables and exponents, which are combined using addition, substraction and mutiplication but not division.

The exponents can only be 0,1,2,3…. etc.

A polynomial cannot have infinite number of terms.

Monomial: A number, a variable or the product of a number and one or more variables.

Polynomial: A monomial or a sum of monomials.

Binomial: A polynomial with exactly two terms.

Trinomial: A polynomial with exactly three terms.

Coefficient: A numerical factor in a term of an algebraic expression.

Degree of a monomial: The sum of the exponents of all of the variables in the monomial.

Degree of a polynomial in one variable: The largest exponent of that variable.

Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order.

What is the degree of the monomial?

245 bx The degree of a monomial is the sum of the exponents of the variables in the monomial.

The exponents of each variable are 4 and 2. 4+2 = 6.

The degree of the monomial is 6.

The monomial can be referred to as a sixth degree monomial.

A polynomial is a monomial or the sum of monomials

24x 83 3 x 1425 2 xx Each monomial in a polynomial is a term of the polynomial.

The number factor of a term is called the coefficient.

The coefficient of the first term in a polynomial is the lead coefficient.

A polynomial with two terms is called a binomial.

A polynomial with three terms is called a trinomial.

ZEROES OF A POLYNOMIAL

A real number α is a zero of a polynomial f(x), if

f(α) = 0.e.g. f(x) = x³ - 6x² +11x -

6f(2) = 2³ -6 X 2² +11 X 2

– 6= 0 .

Hence 2 is a zero of f(x).

The number of zeroes of the polynomial is the

degree of the polynomial. Therefore a quadratic

polynomial has 2 zeroes and cubic 3 zeroes.

14 x

83 3 x

1425 2 xx

The degree of a polynomial in one variable is the largest exponent of that variable.

2 A constant has no variable. It is a 0 degree polynomial.

This is a 1st degree polynomial. 1st degree polynomials are linear.

This is a 2nd degree polynomial. 2nd degree polynomials are quadratic.

This is a 3rd degree polynomial. 3rd degree polynomials are cubic.

Classify the polynomials by degree and number of terms.

Polynomial

a.

b.

c.

d.

5

42 x

xx 23

14 23 xx

DegreeClassify by

degree

Classify by number of

terms

Zero Constant Monomial

First Linear Binomial

Second Quadratic Binomial

Third Cubic Trinomial

To rewrite a polynomial in standard form, rearrange the terms of the polynomial starting with the largest degree term and ending with the lowest degree term.

The leading coefficient, the coefficient of the first term in a polynomial written in standard form, should be positive.

Function Of Polynomial

For it to be a Polynomial Function the exponent has to be positive and whole.

There are 2 forms. Standard Form where it’s all multiplied out. Factored Form where it has parenthesis.

Degree- the highest power of x when it’s in Standard Form.

Leading Coefficient- the first coefficient when the polynomial is in Standard Form and in order. To find the leading coefficient you have to put the polynomial in order by exponent, from highest to lowest.

The x-intercept of the graph and the zero of its function are opposites.

If 2 of the factors are the same then there is only one x-intercept. 2 of the same factors is called multiplicity.

The number of x-intercepts can equal or be less than the number of factors. Never more.

First degree polynomials have one set of parenthesis.

Second degree polynomials have two sets of parenthesis.

Third degree polynomials have three sets of parenthesis.

Fourth degree polynomials have four sets of parenthesis.

745 24 xxx

x544x 2x 7

Write the polynomials in standard form.

243 5572 xxxx

32x4x 7x525x

)7552(1 234 xxxx

32x4x 7x525x

Remember: The lead coefficient should be positive in standard

form.

To do this, multiply the polynomial by –1 using

the distributive property.

Write the polynomials in standard form and identify the polynomial by degree and number of terms.

23 237 xx 1.

2. xx 231 2

23 237 xx

23 237 xx

33x 22x 7

7231 23 xx

723 23 xx

This is a 3rd degree, or cubic, trinomial.

xx 231 2

xx 231 2

23x x2 1

This is a 2nd degree, or quadratic, trinomial.

Thank

You