Factorisation

Introduction to Factorization

Type I-Factorisation by common factor

1. Consider the expression 3x3−15x2+12x.

In all the term, 3x is taken commonly outside.

(3x×x2)+(3x ×−5x)+(3x×4)

=3x(x2−5x+4)

2.  Consider the expression 10xy+5x 3y.

Here the term 5xy is common in the expression. 

10xy+5x 3y

=(5xy×2+5xy×x2)=5xy(2+x2)

Type II-Factorisation by common binomial factor

Consider (n2+1)(m−n)+(m2+1)(m−n).

Take binomial factor from each term commonly outside.

(n2+1)(m−n) +(m2+1)(m−n)

=(m−n)(n2+1+m2+1)

=(m−n)(n 2+m2+2)

Type III-Factorisation by grouping

Consider the expression 3m2 +mn+3mn+n2.

Let us take the common factor for the first two terms separately and take the common factor second two terms separately. 

3m2+mn+3mn+n2

=m(3m+n)+n(3m+n)

=(3m+n)(m+n)

Type IV-Factorisation using identities

Use the following identities to factorise the expressions.

 

Type V- Factorisation of expression in Quadratic form

Procedure to factorise the expression

Step 1: Determine the coefficient a,b and c.

Step 2: Calculate the product of a and c. Product =ac and sum =b. Thus the middle coefficient is the sum and extreme product is the product value.

Step 3: Express the middle term as sum of two terms such that the sum satisfies the middle term and the product satisfies the extreme product.

Step 4:  Now group the expression into two factors by taking the common expression outside.

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