POWER POINT PRESENTATION FOR CLASS X MATHEMATICS - Kar

[Pages:29]POWER POINT PRESENTATION FOR

CLASS X MATHEMATICS

SATHEESH KUMAR K TGT, AECS-5,MUMBAI

CHAPTER TWO

POLYNOMIALS

TOPICS

Introduction Geometrical Meaning of the

Zeros of a Polynomial Relationship Between Zeros

and Coefficients of a Polynomial Division Algorithm for Polynomials

2.1 INTRODUCTION

Definition : An algebraic expression is an expression built up from constants, variables and the algebraic operations(addition, subtraction multiplication and division)

for example : x+3, 3y-8, 7x?, 5xy+8z-3z? etc

Consider the expression 5x? - 4xyz + 8

In this expression 5x?, - 4xyz and 8 are the terms.

Terms are added to form expressions.

Terms themselves are formed as product of factors.

In general, any expression containing one or more terms with non zero coefficients (and variables with non negative integers as exponents) is called a polynomial.

TYPES OF POLYNOMIAL(NO. OF TERMS)

A polynomial of one term is called a monomial.

Examples: 2x, 3xyz, -5, ? z etc A polynomial of two terms is called a

binomial. Examples: 5y-3, 4z?+7, 5xyz ?x etc A polynomial of three terms is called. a trinomial Examples:90xz+16x -?, x-y-7,

2ax +3by ?xy etc

DEGREE OF A POLYNOMIAL The highest power of the variable in a polynomial is the degree of the polynomial. So, the degree of the polynomial 3x7+ 6x4- 4x +8 is 7 and the degree of the polynomial 5y6 + 9y3 ? 10 is 6.

The degree of a non-zero constant polynomial is zero.

TYPES OF POLYNOMIALS (DEGREE)

A polynomial of degree one is called a linear polynomial.

Examples: 3x-5, 8x+7y-9z, ? x-6z-102 etc A polynomial of degree two is called a quadratic

polynomial. Examples: 3x?-5x+4, 8xy+7y-9z, ? x-6z?- etc

A polynomial of degree three is called a cubic polynomial Examples: x?+13x?-5x+14, 8xy+7y-9z?, x-6z?-8y?

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