This document provides an overview of polynomials for a 9th grade math class. It defines what a polynomial is, noting they can have constants, variables, and exponents but no division by variables. It provides examples of polynomials and non-polynomials. It also defines monomials, binomials, and trinomials based on the number of terms. The document explains coefficients of polynomials and the degree of polynomials, defining linear, quadratic, and cubic polynomials based on their degree. The teacher concludes by announcing the next lesson will be on zeroes of polynomials.

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