INTRODUCTION

NAME – SIDDHARTH JAIN

CLASS – 9th

SECTION – C

ROLL NO. – 9304

SUBJECT - MATHS

POLYNOMIALS

Introduction Constant :-component which never change its value or magnitude is known as constant for example all real no. Are always constant as they never changes its values.

Variable :-component of any term or expression or equation which varies situation is known as variable.

Term :-term is an element which is combination of 4 signs , numbers , variable and power or a term always has 4 things sign + or-

Types of terms

Like terms – two or more having same type of variable and same power on them are said to be like terms for example 3x ,-7/2x,8/9x , are like terms.

Unlike terms –terms if they are not like then they are known as unlike terms for example 7a , 8b , 19/3c are unlike terms.

What is polynomials ?An algebraic expression in the form of : 2a2 +3b+5c+6x,…..+…….

Different types of polynomials:-

1.Monomial :-expression have single term.

2.Binomial :- expression have two terms.

3.Trinomial :-expression have three term.

4. Multinoamil :-expression have more than three terms.

5.Zero polynomial:-number itself is known as zero polynomial.

Degree of a polynomial

1.Linear polynomial :- A polynomial of the form ;ax + b, a = 0 is known as linear polynomial its degree is always zero it may be monomial or binomial . It may be monomial or binomial for example each of polynomial 2x , -3x is a linear polynomial as well as monomial and linear polynomial.

2. Quadratic polynomial :- an algebraic expression of type ax2 +bx +c,a is not equal 0 is known as quadraic polynomial, or we can say that polynomial of degree2 is known as quadraic polynomial, quadratic polynomial can be a monomial , binomial or trinomial.

3. cubic polynomials – a polynomial of the form of ax3+bx2+cx+d , a=0 is known as cubic polynomial . A cubic polynomial may be monomial , binomial , trinomial , multinomial .

VALUE AND ZEROES OF POLYNOMIAL

Value of a polynomial

The value of a polynomial p(x) at x = a is p(a) . Obtained on replacing x by a . Zeroes of a polynomial

In general we say that (a) is a zero of polynomial p(x) at a such that p(a)=0 .

Factor theorem

Let p{x} be any polynomial of greater than or equal to 1 and “a” be any real number , , then

i. {x-a} is a factor of p{x}, if p{a}=0;and

ii. P{a]=0 if {x-a}is a factor of p{x}.

iii. Proof :let p{x} be a polynomial of degree n >1 and “a” be a real number.

iv. If p {a} =0 {given}

v. Let q{x] be the quotient when p{x} be divided by {x-a}.

vi. By reminder theorem , remainder =p{a}

vii. Polynomial= divisor* quoient +remainder

viii. p{x}={x-a} q{x}+p{a}=p{x}=[x-a]q[x]:p{a}=0 proved

IDENTITIES (a + b)2 = a2 + 2ab + b2

(a – b)2 = a +a2 – 2ab + b2

a2 – b2 = ( b)(a – b) (x + a)(x + b) = x2 + (a + b)x + ab (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca (a + b)3 = a3 + b3 + 3ab (a + b) (a – b)3 = a3 – b3 – 3ab (a – b) a3 + b3 = (a + b)(a2 – ab + b2) a3 – b3 = (a – b)(a2 + ab + b2) a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca) a3 + b3 + c3 = 3abc , If a + b + c = 0

Important points to remember :

A constant polynomial does not has any zero .

0 may be a zero of a polynomial . Every linear polynomial has one and only

one zero . A polynomial can have repeated zeroes . Number of zeroes of a polynomial cannot

exceed its degree.

THANKS