Factorization
Factorization is a process of splitting any given polynomial into possible factors. If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.
If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial.
There are a number of methods followed for factorization. Some of them are as follows:
(i) Common factors
(ii) By expressing as difference of squares
(iii) By grouping
(iv) Trinomials
(v) Sum or difference of cubes
1. Taking out Common Factors
8a3 b - 6a2b2 = 2a2b (4a - 3b)
In the above expression, we are taking out the term 2a2b, since it is common to both the terms and thus we are factoring the equation to a simplified form.
2. Expressing Polynomial as Difference of Two Squares
121x2 - 25y2 = (11x)2 - (5y)2
= (11x + 5y) (11x - 5y) [Using the identity a2-b2=(a-b)(a+b)]
This is another way to simplify an equation.
Factorization tree is more easier to understand and construct. It is very helpful in finding prime factors of a bigger number.- The digit in unit's place of 18 is 8, which is an even number so is divisible by 2. So we factorize by 2
- Check the numbers so obtained. If both the factors are prime then stop factorization
- If any one of them is not a prime factor, then check the unit's digit of the number.
- If the number in unit's place is not divisible by 2 then start with 3, if not with 3 then try divisibility by 5,7.
- Follow the above steps again until we get all factors of 18 as prime factor
Below you could see polynomial factorization
Solved Examples
Solution:
Solution:
Solved Examples
Solution:
Then the given expression
= (x)2 - (7b)2
= (x + 7b) (x - 7b)
Re-substituting the value of x, we get
= [(5a + 6b + 7b)] [(5a + 6b) - 7b]
= (5a + 6b + 7b) (5a + 6b - 7b)
= (5a + 13b) (5a - b)
Solution:
