1. Factorising quadratics
6x2 + x - 2
is in the form ax2 + bx + c
So a = 6, b = 1, c = -2
You need to find 2 numbers which multiply to give ac (in this case -12) and add to give b (in this case +1)
Now list the factors of ac

2. 1
-12 -1 12 2 -6 -2 6 3 -4 -3 4 -3 4
Decide which pair adds up to b ie +1
Replace the x term by these two values ie -3x and 4x
so 6x2 + x – 2 becomes 6x2 + 4x -3x -2
Now factorise it as a four term expression

3. 6x2 + 4x -3x -2
= 2x (3x + 2)
+1 (-3x - 2)
There is nothing common in the second part so take out +1
Unfortunately, the signs in the second bracket are – those in the first bracket
So instead of taking out +1 we take out -1
= 2x (3x + 2) -1 (3x + 2)
The brackets are now the same so take them out as common factors
So 6x2 + x - 2= ( 3x + 2 ) ( 2x -1 )

4. 6x2 + 4x -3x -2
= 2x (3x + 2)
+1 (-3x - 2)
= 2x (3x + 2) -1 (3x + 2)
So 6x2 + x - 2= ( 3x + 2 ) ( 2x -1 )
check
F O I L
6x2
-3x
+4x -2
= 6x2 + x - 2