1. x2 + x - 12 = x2 + 4x - 3x - 12
= x(x + 4) - 3(x + 4)
= (x - 3)(x + 4)
2. x2 - x - 12 = x2 - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
= (x + 3)(x - 4)
3. x2 + 4x - 12 = x2 + 6x - 2x - 12
= x(x + 6) - 2(x + 6)
= (x - 2)(x + 6)
4. x2 + 8x + 15 = x2 + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 5)(x + 3)
5. 5x2 - 4x - 1 = 5x2 - 5x + x - 1
= 5x(x - 1) + (x - 1)
= (5x + 1)(x - 1)