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CHAPTER 1
REAL NUMBERS


1. A number is prime if it has only two factors, 1 and itself.
2. Every composite number can be expressed as a product
of prime factors.



B
3. H C F of two numbers = Product of the smaller power of
each common factor in the numbers.
U
H.C.F. of (30, 45) = 3 x 5 = 15. [30 = 2 x 3 x 5 ;45 = 32 x 5]
PH
4. L C M of two numbers = Product of the greatest power
of each prime factor involved in the numbers.
L C M of ( 30, 45 ) = 2 x 32 x 5 = 90
EX


5. 𝐻 𝐶 𝐹 ( 𝑎, 𝑏 ) x 𝐿 𝐶 𝑀 ( 𝑎, 𝑏 ) = 𝑎 x 𝑏
6. 𝐻 𝐶 𝐹 ( 𝑎, 𝑏, 𝑐 ) x 𝐿 𝐶 𝑀 ( 𝑎, 𝑏, 𝑐 ) ≠ 𝑎 x 𝑏 x 𝑐

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CHAPTER 2
POLYNOMIALS
1. x is a variable and 𝑎0 , 𝑎1 , … … … . . 𝑎𝑛 be real numbers, n is a
positive integer then
f(x) = 𝑎0 + 𝑎1 𝑥 + 𝑎2 𝑥 2 + − − − − 𝑎𝑛 𝑥 𝑛 is a polynomial in the
variable of x.
2. The exponent of the highest degree term is called the degree of
the polynomial.



B
3. Constant Polynomial : 𝑓(𝑥) = 𝑎 , a is constant.
U
Linear Polynomial : 𝑓(𝑥) = 𝑎𝑥 + 𝑏 , 𝑎 ≠ 0
Quadratic Polynomial : 𝑓(𝑥)=𝑎𝑥 2 + 𝑏 𝑥 + 𝑐 , 𝑎 ≠ 0
PH

Cubic Polynomial : 𝑓(𝑥) = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐 𝑥 + 𝑑 , 𝑎 ≠ 0
4. A real number ‘a’ is a zero of the polynomial 𝑓(𝑥) 𝑖𝑓 𝑓(𝑎) = 0
EX


5. A polynomial of degree ‘n’ can have at most ‘n’ real zeros.
6. Geometrically, the zeros of the polynomial 𝑓(𝑥) are the 𝑥
coordinates of the points where the graph
𝑦 = 𝑓 (𝑥 ) intersects the 𝑥 axis.
7. If 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the quadratics polynomial 𝑓(𝑥)
= 𝑎𝑥 2 + 𝑏 𝑥 + 𝑐 , 𝑡ℎ𝑒𝑛
𝑏
Sum of the Zeros = 𝜶 + 𝜷 = −
𝑎
𝑐
Product of the Zeros = 𝜶 𝜷 =
𝑎