Factorise 6x2 + x - 2 = 0
- Firstly, multiply the coefficient of x2 by the last number:
6 x -2 = -12
- List all the factors of 12 and see which pair adds/subtracts to make 1:
Factors of 12: [1,12] [2,6] [3,4] -----------> +4 - 3 = 1
- Rewrite the quadratic equation, but split the x up into the above factors:
6x2 + 4x - 3x - 2 = 0
- Split the equation in half:
(i) 6x2 + 4x (ii) -3x - 2
- Factorise both halves (hint: both brackets should be the same):
(i) 2x (3x + 2) (ii) -1 (3x + 2)
- Place the numbers outside both brackets together into one bracket:
(2x - 1)
- Final answer:
6x2 + x - 2 = (2x - 1) (3x + 2)