# Factoring

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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.

**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

• Factorization by common factor

• Factorization by Grouping

• Factorizing using Identities

• Factorization of Cubic Polynomial

• Solved Examples on Factorization

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