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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.
The algebraic expressions that may be multiplied to obtain the given algebraic expressions are called factors of the given algebraic expression.
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 15a3
Factors of 15 = 3 x 5
Factors of a3
= a x a x a
Factors of b2
= b x b
∴ Factors of 15a3
= 3 x 5 x a x a x a x b x b
3) Find the factors of 1/2p4
Factors of 1/2 : 1/2
Factors of p4
= p x p x p x p
Factors of q : q
∴ Factors of 1/2p4
q = 1/2 x p x p x p x p x q.
4) Find the factors of 42x3
Factors of 42 : 2 x 3 x 7
Factors of x3
: x . x . x
Factors of y2
: y . y
∴ factors of 423
= 2 x 3 x 7 . x.x.x .y.y
• Factorization by common factor
• Factorization by Grouping
• Factorizing using Identities
• Factorization of Cubic Polynomial
• Solved Examples on Factorization
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