Mathematics IX class state Syllabus

2. 1. The cost of 3 pens and 4 pencils is Rs. 50. Express in
symbolic Form.
+ = 50
A: 3 x + 4y = 50

3. 2. In a Garden the plants are in ‘x’ rows and ‘y’ columns.
How you calculate the total plants? Give Expression.
A: x.y = xy

4. 3. What is the volume of Cuboid?
A: l x d x h = ldh

5. 3x + 4y = 50
xy
Lbh
x2 + 2x + 5
Algebraic Expressions.
These are also called Polynomials
2 2
5x
y
 

7. Polynomials have the Non negative integers as
Exponents of the Variable.
We denote Polynomials as p(x), r(x), t(x) etc.
  1
1 1
n n
n n op x a x a x a x a
    
All of these coefficients are real numbers
n must be a positive integer

8. For Example:
Algebraic Expressions Polynomials
2
1
2
2 2
2
3
3
2 5
x
x
x xy y
x
x

 
 
2
x
2 2
x xy y 
Power is Rational Number
Power is Negative

9. 2
r
1
3 2
2 4 2x x 
2
3 5 2x x 
Polynomial
Not a
Polynomial
Polynomial

10. Degree of Polynomial:
The degree of the polynomial is the
largest power on any x term in the
polynomial.
Ex: 4
2 3 2x x 
2
3 2 5xy xy 
Degree = 4
Degree = 3
(here xy2 = 1+2 = 3)

11. x 0
2
1
xx 
Not a polynomial because of the square root
since the power is NOT an integer
  xxxf  4
2 A polynomial of degree 4.
  2xg
  12  xxh
  23
x
x
xF 
A polynomial of degree 0.
We can write in an x0 since this = 1.
Not a polynomial because of the x in the
denominator since the power is negative
11 
 x
x

12. TYPES OF POLYNOMIALS
ACCORDING TO DEGREE:
0 Zero Polynomial
-12, 5 etc Constant Polynomial
x – 12, ax + b etc Linear Polynomial
Quadratic Polynomial
Cubic Polynomial
2
3 3x x 
3 2
3 2 5 7x x x  

13. ACCORDING TO TERMS:
Monomial
Binomial
Trinomial
Multinomial
2
3 , 2 ,x x x
2
2 1,5 1x x 
2
3 2 1x x 
More than 3 terms