The factor is a number or algebraic expression that divides another number or expression evenly i.e its remainder is 0. (or) factors are small numbers when multiplied gives other numbers. For Example 1, 2, 4, 7, 14, and 28 are factors of number 28.
- Prime factor form: If we write a number in form of the product of prime factors. Then it is called prime factors form.
Example: 70 = 2 * 5 * 7; (here 2, 5, 7 are factors of 70; speacially these are also called prime factors as these (2, 5, 7 are prime numbers)
- Algebraic expression factors: Similarly, we can express algebraic expressions as the product of their factors. If an algebraic expression cannot be reduced further then it is its factor.
Example: 8xy = 8 * x * y (here 8xy is formed by multiplication of numbers(8, x, y) are factors of that number)
Factorization is nothing but writing a number as the product of smaller numbers. It is the decomposition of a number (or) mathematical objects into smaller or simpler numbers/objects. The process includes in factorization are:
1. Method of Common Factors
- Step 1: First, split every term of algebraic expression into irreducible factors
- Step 2: Then find the common terms among them.
- Step 3: Now the product of common terms and the remaining terms give the required factor form.
2. Factorization by Regrouping
Sometimes the terms of the given expression should be arranged in suitable groups in such a way. So that all the groups have a common factor.
3. Factorization using Identities
There are many standard identities. Some of them are given below:
i. (a + b)2 = a2 + 2ab + b2
ii. (a – b)2 = a2 – 2ab + b2
iii. a2 – b2 = (a + b) (a – b)