Q. 44.2( 294 Votes )

Factorize:
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Answer :

For quadratic polynomial. We factorize the middle term such that the product of the terms is equal to the product of the last term and coefficient of x2 and sum or difference is equal to the middle term.

(i)


12x2 - 7x + 1

For the equation given above:

7 is to be factorized such that, the product of two terms is 12 x 1 = 12 and the sum is equal to 7
This can be done by 3 and 4
as 3 x 4 = 12
and 3 + 4 = 7
Therefore,

12x2 - 7x + 1 = 12x2 – 4x – 3x + 1


 = 4x (3x – 1) – 1 (3x – 1)


 = (3x – 1) (4x – 1)


(ii) 

2x+ 7x + 3

For the equation given above:

7 is to be factorized such that, the product of two terms is 3 x 2 = 6 and the sum is equal to 7
This can be done by 6 and 1
as 6 x 1 = 6
and 6 + 1 = 7
Therefore,

2x+ 7x + 3 = 2x2 + 6x + x + 3


= 2x (x + 3) + 1 (x + 3)


 = (x + 3) (2x + 1)


(iii)

6x2 + 5x – 6

For the equation given above:

7 is to be factorized such that, the product of two terms is 6 x 6 = 36 and the difference is equal to 5
This can be done by 9 and 4
as 9 x 4 = 36
and 9 - 4 = 5
Therefore,

6x2 + 5x – 6 = 6x2 + 9x – 4x – 6


 = 3x (2x + 3) – 2 (2x + 3)


 = (2x + 3) (3x – 2)


(iv)

3x2 - x - 4

For the equation given above:

7 is to be factorized such that, the product of two terms is 4 x 3 = 12 and the difference = 1
This can be done by 4 and 3
as 4 x 3 = 12
and 4 - 3 = 1
Therefore,

3x2 - x - 4=3x2 – 4x + 3x – 4


= x (3x – 4) + 1 (3x – 4)


= (3x – 4) (x + 1)

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