(i) Let p(x) = 3x² + 7x + 2

Here we have to split middle term of p(x)

i.e. 7 into two parts such that their sum is 7 and product is 2 x 3 = 6.

6 and 1 are such numbers whose sum is 7 and product is 6

∴ 3x² + 7x + 2 = 3x² + 6x + x + 2

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

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

(ii) Let p(x) = 4x² – x – 3

Here we have to split middle term – 1 into two parts such that their sum is – 1 product is 

3 × – 4 = – 12

– 4 and 3 are such numbers whose sum is – 1 and product is – 12

4x² – x – 3 = 4x² – 4x + 3x – 3

= 4x(x – 1) + 3(x – 1)

= (x – 1 )(4x + 3)

(iii) Let p(x) = 12x² – 7x + 1

Here we have to split middle term – 7 into two parts such that their sum is – 7 and product is 

12 × 1 = 12

  – 4 and – 3 are such numbers whose sum is – 7 and product is 12

12x² – 7x + 1 = 12x² – 4x – 3x + 1

= 4x(3x – 1) – 1(3x – 1)

= (3x – 1)(4x – 1)

(iv) Let p(x) = 6x² + 5x – 6

Here we have to split middle term 5 into two parts such that their sum is 5 and product is 

6 × – 6 = – 36

9 and – 4 are such numbers whose sum is 5 and product is – 36. .

6x² + 5x – 6 

= 6x² + 9x – 5x – 6

= 3x(2x + 3) – 2(2x + 3) 

= (2x + 3)(3x – 2)