Question

Explain :
1. Finding factors
2.Finding Common factors

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Answer 1

QuestioN :

Explain :

1. Finding factors

2.Finding Common factors

ANswer :

1).

* Factorising a monomial : Factors of a given monomial are represented by the prime factorisation of the coefficient of the given monomial and repeated multiplication of the variable / s on the basis of degree.

10 = 2 × 5

Here, 2 is a factor of 10, 5 is a factor of 10.

3x = 3 × x

Here, 3 is a factor of 3x, x is a factor of 3x.

6x²y² = 2 × 3 × x × x × y × y

Here, 2, 3, x, x, y and y are factors of 6x²y².

Examples :

* Factorise the following monomials :

[ 1 ] 15x²y

15x²y = 3 × 5 × x × x × y

[ 2 ] 12xy³

12xy³ = 2 × 2 × 3 × x × y × y × y

2).

* Factorizing a binomial [ method of taking common factor ] :

ab + ac = ab + ac

         = a ( b+c ) [ a is a common factor ]

Here, a and ( b+c) are the factors of ab+ ac.

3x²y + 2x = x [ 3xy + 2 ]

Here, x and ( 3xy + 2 ) are the factors of 3x²y + 2x.

Examples :

* Factorise the following binomials :

[ 1 ] 2xy + 4

     = 2 ( xy +2 )

[ 2 ] 8x + 12

      = 4 ( 2x + 3 )

[ 3 ] 6a²b - 3ab²

       = 3ab ( 2a - b )

[ 4 ] 5x²y - 15y²

       = 5y ( x²-3y )

Hope this will help you :-)