(i) 12x2 - 7x + 1
= 12x2 - (4 + 3)x + 1
= 12x2 -4x -3x + 1
= 4x(3x - 1) -1(3x - 1)
= (3x - 1)(4x - 1)
Hence, 12x2 - 7x + 1 = (3x - 1)(4x - 1)
(ii) 2x2 + 7x + 3
= 2x2 + (6 + 1)x + 3
= 2x2 + 6x + x + 3
= 2x(x + 3) + 1(x + 3)
= (2x + 1)(x + 3)
Hence, 2x2 + 7x + 3 = (2x + 1)(x + 3)
(iii) 6x2 + 5x - 6
= 6x2 + (9 - 4)x - 6
= 6x2 +9x - 4x - 6
= 3x(2x + 3) -2(2x + 3)
= (2x + 3)(3x - 2)
Hence, 6x2 + 5x - 6 = (2x + 3)(3x - 2)
(iv) 3x2 - x - 4
= 3x2 - (4 - 3)x - 4
= 3x2 - 4x + 3x - 4
= x(3x - 4) + 1(3x - 4)
= (3x - 4)(x + 1)
Hence, 3x2 - x - 4 = (3x - 4)(x + 1)