Question

can anyone say important topics and formulas from polynomials and factorisation chapter....

Answer 1

IMPORTANT TOPICS ARE
1. ZEROES OF POLYNOMIALS
2. IDENTITIES

They ask twisted question from these two topics. Hope i has helped you.

Answer 2

REAL NUMBERS

·         Euclid’s division lemma: given positive integers a and b, there exists unique integer q and r satisfying a=bq+r, 0≤r<b

·         Fundamental theorem of arithmetic: every composite number can be expressed as a product of prime and this factorisation is unique apart from the order in which the prime factors occur                  [HCF*LCM=Product of two numbers]

·         Theorem 1.3: let p be a prime number. If p divides a2, then p divides a, where a is a positive integer

·         Theorem1.4:  is irrational

·         Theorem1.5: let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form p/q where p and q are coprime and prime factorisation of q is of the form 2n5m, where n, m are non-negative integers

·         Theorem1.6: let x=p/q be a rational number, such that the prime factorisation of q is of the form 2n5m where n, m are non-negative integer. Then x has decimal expansion which terminates

·         Theorem1.7: let x=p/q be a rational number, such that the prime factorisation of q is  not of the form 2n5m  where n, m are non-negative integer. Then x has decimal expansion which is non-terminating(recurring)

Polynomials

·         Quadratic                                 cubic

1.      α+β= -b/a                             α+β+ϒ = -b/a

2.    αβ = c/a                                       αβ+βϒ+ϒα = c/a

                                                     αβϒ = -d/a

·         Required polynomial:  x2 -(α+β)x +αβ

·         P(x)=g(x)*q(x)+r(x),where  r(x)=0 or degree r(x)<degree g(x)