introdution of polynomials :- Basic concept of polynomials with examples

1. Polynomials
CLASS- 9th
Faculty - Nikhil Patel
MATHS
Reference Book :- NCERT Class 9th

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3. Polynomials
Class-IX
Introduction
Basic concept of Polynomials
&
Tips and tricks of
remember
The concepts of polynomials
With examples

4. Polynomials
Class-IX
Many terms
Constant
Variables
Exponents
A polynomial can have:-
• Constants (like 2, 5, or 6)
• Variables (like x and y)
• Exponents (like the 2 in 2),
but only 0, 1, 2, 3, ...Etc are allowed
that can be combined using addition,
subtraction, multiplication & division ...
Polynomial comes from poly (meaning "many") and nomial
(meaning "term") so it says "many terms"

5. Polynomials
Class-IX
"A polynomial can have constants, variables and but never
division by a variable.
Polynomial or Not ?
Exponent
Terms
A Polynomial Not Polynomial
•3x
•x − 2
•−6y2 − (79)x
•5
• 3xy-2
• 2/(x+2)
• 1/x
• √x
• x/2 is allowed, because you can divide by
a constant
• 3x/8 is allowed for the same reason
• √2 is allowed, because it is a constant(=1.4142..)
A Polynomial Not Polynomial
Some other examples

6. Polynomials
Class-IX
Polynomials can have :-
No variable or Zero polynomial
2 is a polynomial. It has just one term, which is a
constant and it is also called the zero polynomial.
One variable
 x4 − 2x2 + x has three terms, but only one variable (x)
Two or more variables
xy4 − 5x2z has two terms, and three variables (x, y & z)
Variables
3xy2
5
x² + 7x -2= 0
No variable or zero polynomial
One variable (x)
Two variable (X,Y)

7. Polynomials
Class-IX
There are special names for polynomials with 1, 2 or 3
terms:
Monomial, Binomial, Trinomial
Polynomials having only three terms are called
Trinomials (‘tri’ means ‘three’).
Polynomials having only one term are called
Monomials (‘mono’ means ‘one’).
Polynomials having only two terms are called
Binomials (‘bi’ means ‘two’).
How do you remember the
names? Think cycles!
Bicycle
Tricycle
Monocycle

8. Polynomials
Class-IX
The coefficient of x³is 1,
 Coefficient of X²is 4,
 Coefficient of x is 7 &
 –2 is coefficient of x0
Coefficient of Polynomials
4 x² + 2 x +
7
Coefficient of X²is 4
Coefficient of X is 2
Coefficient of X0 is 7
x³+ 4x² + 7x – 2
Each term of a polynomial has a Coefficient.

9. Polynomials
Class-IX
“The highest power of x in polynomial P(x) is called the Degree Of Polynomial P(x).
 LINEAR POLYNOMIAL:- A polynomial of degree
1 is called a LINEAR POLYNOMIAL
Example:- 2X-3 ,Y-√4 ,√3x-5 , X-2/11 , Etc…
QUADRATIC POLYNOMIAL:- A polynomial of degree
2 is called QUADRATIC POLYNOMIAL
Example :- X², 2X²+3X-2/5, Y²-2 , 2-X², Etc…
 CUBIC POLYNOMIAL :- A polynomials of degree
3 is called CUBIC POLYNOMIAL
Example:- 2-x³, x³,√2x³, 3-x²+x³, Etc…
Degree of P(x)= 1
Degree of P(x)= 2
Degree of P(x)= 3
Degree Of Polynomials

10. Thank you !!!

11. Zeroes of a Polynomials
Next lesson of polynomials