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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.

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

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