best of all from NITISH

3. WE THE STUDENTS OF CLASS
IX HAVE TRIED OUR BEST TO
DO THE PRESENTATION IN
SUCH A WAY THAT THIS
REPRESENTATION WOULD BE
THE BEST ONE

4.  In mathematics, a polynomial is an expression consisting of variables
(or indeterminate) and coefficients, that involves only the operations
of addition, subtraction, multiplication, and non-negative integer
exponents. An example of a polynomial of a single indeterminate (or
variable), x, is x2 − 4x + 7, which is a quadratic polynomial.
 Polynomials appear in a wide variety of areas of mathematics and
science. For example, they are used to form polynomial equations,
which encode a wide range of problems, from elementary word
problems to complicated problems in the sciences; they are used to
define polynomial functions, which appear in settings ranging from
basic chemistry and physics to economics and social science; they are
used in calculus and numerical analysis to approximate other
functions. In advanced mathematics, polynomials are used to
construct polynomial rings and algebraic varieties, central concepts
in algebra and algebraic geometry.

5. WE HAVE TRIED OUR BEST TO PREPARE
THE PROJECT. WE WANT TO THANKS ALL
THE MEMBERS OF OUR GROUP FOR
HAVING A GOOD RESPOND FOR THE
PROJECT WHICH INSPIRED ALL.AT THE
BUT NOT THE LEAST….WE RESPECTFULLY
THANKS OUR TEACHER FOR GIVING
SOME IDEA ABOUT THE PROJECT.

6. • Polynomials
An expression containing variables, constant and
any arithematic operation iscalled polynomial.
Polynomial comes
from po ly- (meaning "many") and -
no mial (in thiscasemeaning
"term") ... so it says"many terms"

7. • Polynomialscontain threetypesof terms:-
(1) monomial :- A polynomial with oneterm.
(2) binomial :- A polynomial with two terms.
(3) trinomial :- A polynomial with threeterms.

8. • Degreeof polynomial :- thehighest power of the
variablein apolynomial istermed asthedegreeof
polynomial.
• Constant polynomial :- A polynomial of degreezero is
called constant polynomial.
• Linear polynomial :- A polynomial of degreeone.
• E.g. :-9x + 1
• Quadratic polynomial :- A polynomial of degree two.
E.g. :-3/2y² -3y + 3
• Cubic polynomial :- A polynomial of degreethree.
• E.g. :-12x³ -4x² + 5x +1
• Bi – quadratic polynomial :- A
polynomial of degree four.
• E.g. :- 10x – 7x ³+ 8x² -12x + 20

9. • . Standard Form
• The Standard Form for writing apolynomial isto put
thetermswith thehighest degreefirst.
• Example: Put this in Standard Form: 3x2
- 7 +
4x3
+ x6
Thehighest degreeis6, so that goesfirst, then 3, 2
and then theconstant last:
x6
+ 4x3
+ 3x2
- 7

10. • Let p(x) beany polynomial of degree
greater than or equal to oneand let a
beany real number. If p(x) isdivided
by linear polynomial x-athen the
reminder isp(a).
• Proof :- Let p(x) beany polynomial of
degreegreater than or equal to 1. suppose
that when p(x) isdivided by x-a, the
quotient isq(x) and thereminder isr(x), i.g;
p(x) = (x-a) q(x) +r(x)
Remindertheorem

11. Sincethedegreeof x-ais1 and thedegreeof r(x) is
lessthan thedegreeof x-a,thedegreeof r(x) = 0.
Thismeansthat r(x) isaconstant .say r.
So , for every valueof x, r(x) = r.
Therefore, p(x) = (x-a) q(x) + r
In particular, if x = a, thisequation givesus
p(a) =(a-a) q(a) + r
Which provesthetheorem.

12. Let p(x) beapolynomial of
degreen > 1 and let abeany
real number. If p(a) = 0 then
(x-a) isafactor of p(x).
PROOF:-By thereminder
theorem ,
p(x) = (x-a) q(x) + p(a).
FactorTheorem

13. 1. If p(a) = 0,then p(x) = (x-a) q(x), which
showsthat x-aisafactor of p(x).
2. Sincex-aisafactor of p(x),
p(x) = (x-a) g(x) for samepolynomial
g(x).
In thiscase, p(a) = (a-a) g(a) =0

16. Therefore our
beauTiful projecT ends
hope This projecT
would help us To geT
beTTer marks, which
has became a greaT
Task for us, in The pasT

17.  We have collected the information from books and
reference books to present the project successfully in
the presentation.
The clip art photos used in the Power Point
presentation are brought from the world wide web.
 THANK YOU

18. THANKYOU