group dynamics theory

In many situations, we come across polynomials, which may not have common factors among its terms. In such cases, we group the terms of the expression in such a way that there are common factors among the terms of the groups so formed. Let us study such exampl..

There are various methods of factorising a polynomial. They are, 1. Factorisation by dividing the expression by the HCF of the terms of the given expression. 2. Factorisation by grouping the terms of the expression. 3. Factorisation using identities. Let us study these methods one after ..

Identify the HCF of the terms of the groups. Now, observe that, (2x - 3a) is a common factor for both the groups. Therefore (2x - 3a) is one of the factors of the given expression. The other factor is identified by dividing each group by the common factor i.e. (..

There are various methods of factorising a polynomial. They are, Factorisation by dividing the expression by the HCF of the terms of the given expression. Factorisation by grouping the terms of the expression. Factorisation using identitie..

Find all pairs of factors whose product is the last term of the trinomial. From the pairs of factors from step 1, choose a pair of factors whose sum is the coefficient of the middle term of the trinomial. Split the middle term using the pair of factors from step 2 and rewrite the trino..

Step 1: Factor pairs of the last term are (-7,+3), (21,-1), (+7,-3), (-21,+1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (+7,-3). Step3: Rewrite the expression using these factors as w 2 + 7w - 3w -21. Step 4: Group the terms and factorise...

Find 'a.c ', the product of the coefficient of x 2 and the last term. Find all the factor pairs of 12. (1,12), (3,4), (2,6) are the factor pairs of 12. The factor pair (3,4) is such that 3 + 4 = 7and 3 x 4 = 12 i.e, sum of the numbers is equal to the coefficient of the middle term(b), and the..

Many theories have been proposed to explain the process of ageing. The important ones have been listed. The theories of Ageing have been grouped into two categorie..

. As a result, a large number of energy levels are crowded together into 'bands'. Because of these energy bands, the molecular orbital theory of metals is also known as band theory. As an illustration the bonding in sodium metal can be studied. Imagine that a crystal of sodium i..

Example: In the complex between CoCl 3 and NH 3 the ionizable chloride ions are found by precipitation with AgNO 3 . The remaining Cl and NH 3 are present around the central Co in such directions so as to minimize repulsion and are linked by secondary valencies. a) Primary valencies - represented b..