(i) 12x²–7x+1

Using the splitting the middle term method,

We have to find a number whose sum = -7 and product = 1 × 12 = 12

We get -3 and -4 as the numbers [-3 + -4 = -7 and -3 × -4 = 12]

12x²–7x+1 = 12x²-4x-3x+1

= 4 x (3x-1) - 1(3x-1)

= (4x-1)(3x-1)

(ii) 2x²+7x+3

Using the splitting the middle term method,

We have to find a number whose sum = 7 and product = 2 × 3 = 6

We get 6 and 1 as the numbers [6+1 = 7 and 6×1 = 6]

2x²+7x+3 = 2x²+6x+1x+3

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

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