# Factoring

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Factoring : It is the process of writing an algebraic expression, as the product of two or more algebraic expressions.

30 = 2 × 15
= 3 × 10 = 5 × 6
Thus, 1, 2, 3, 5, 6, 10, 15 and 30 are the factors of 30.
Of these, 2, 3 and 5 are the prime factors of 30 because we can not find the factors of 2,3 and 5 further.

Factorize is the reverse of expand i.e. put in brackets.

Factors : The algebraic expressions that may be multiplied to obtain the given algebraic expressions are called factors of the given algebraic expression.

Examples :

1) Find the factors of 8xy.
Solution :
Factors of 8 : 2 x 2 x 2
Factors of x : x
Factors of y : y
∴ factors of 8xy = 2 x 2 x 2 . x .y

2) Find the factors of 15a
3 b 2 .

Solution :
Factors of 15 = 3 x 5
Factors of a
3 = a x a x a
Factors of b
2 = b x b
∴ Factors of 15a
3 b 2 = 3 x 5 x a x a x a x b x b

3) Find the factors of 1/2p
4 q.

Solution :
Factors of 1/2 : 1/2
Factors of p
4 = p x p x p x p
Factors of q : q
∴ Factors of 1/2p
4 q = 1/2 x p x p x p x p x q.

4) Find the factors of 42x
3 y 2 .
Solution :
Factors of 42 : 2 x 3 x 7
Factors of x
3 : x . x . x
Factors of y
2 : y . y
∴ factors of 42
3 xy 2 = 2 x 3 x 7 . x.x.x .y.y

Factoring

Factorization by common factor
Factorization by Grouping
Factorizing using Identities
Factorization of Cubic Polynomial
Solved Examples on Factorization