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

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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.

1) Find the factors of 8xy.

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

Factors of 15 = 3 x 5

Factors of a

Factors of b

∴ Factors of 15a

3) Find the factors of 1/2p

Factors of 1/2 : 1/2

Factors of p

Factors of q : q

∴ Factors of 1/2p

4) Find the factors of 42x

Factors of 42 : 2 x 3 x 7

Factors of x

Factors of y

∴ factors of 42

• Factorization by common factor

• Factorization by Grouping

• Factorizing using Identities

• Factorization of Cubic Polynomial

• Solved Examples on Factorization