presentation on chapter 2 of 9th maths , polynomials basic things - factor theorem , identities , knowledge of polynomials

1. INTRODUCTION
NAME – SIDDHARTH
JAIN
CLASS – 9th
SECTION – C
ROLL NO. – 9304
SUBJECT - MATHS

3. 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-

4. 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.

5. 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.

6. 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

7. 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 .

8. 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 .

9. 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

10. 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

11. 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.