Quant Ready Recokner-The ultimate formula booklet

Methods of Finding Factors:

1. Taking Out Common Factors: Place the common factor outside as a coefficient and divide each term separately by same factor.

2. Factors by Grouping the Terms: An expression having even number of terms may be resolved into factors if the terms are arranged in groups such that each group has a common factor.

Factorizing the Trinomials of The form ax² + bx + c:

If the product ‘ac’ is positive, find two numbers whose sum is ‘b’ and product is ‘ac’. If the product ‘ac’ is negative, find two numbers whose difference is ‘b’ and product is ‘ac’. Then rewrite equation replacing b by sum (difference) of a and c.

Factorization of the Sum of or Difference of Two Cubes:

If ‘a’ is a rational number and ‘n’ is a positive integer such that the nth root of ‘a’ is an irrational number, then a^1/n is called a surd e.g.,  Ö5,Ö3, Ö2 etc.

If  a^1/n  is a surd then ‘n’ is known as order of surd and ‘a’ is known as radicand.

Every surd is an irrational number but every irrational number is not a surd.

Rational Indices:

a × a × a ……. m factors = a^m

Here, ‘a’ is called the base and m is called the index or power or exponent of ‘a’.

Law of Indices:

1. A number will be divisible by 2 iff the digit at the unit place is divisible by 2.

2. A number will be divisible by 3 iff the sum of digits of the number is divisible by 3

3. A number will be divisible by 4 iff last two digits of the number together are divisible by 4.

4. A number will be divisible by 5 iff digit at the unit place is either 0 or 5.

5. A number will be divisible by 6 iff the digit at the unit place of the number is divisible by 2 & sum of all digits of the number is divisible by 3.

6. Divisibility test of 7: Make two set of three nos. starts from unit digit then add the alternate sets, and find out the mutual difference, if it is 0 or any multiple of 7 then the given no. is divisible by 7.

e.g.,   001234567