Question

How do you factor 6x² - x - 2?

Answer 1

Let's use the AC Method.

First multiply the coefficient (`A=6`) of the `x^2` term by the coefficient (`C=2`) of the constant term - ignoring the sign.

`AC = 6*2 = 12`

Notice that the sign of the constant (`C`) term is negative.

According to the AC Method, we need to look for a factorisation of our `AC` value into a pair of factors, whose difference is the middle coefficient `B=1`. Well `4 xx 3 = 12` and `4 - 3 = 1`. So the pair we want is `4` and `3`.

Now use this pair to split the middle term then factor by grouping:

`6x^2-x-2 = 6x^2-4x+3x-2`

`= (6x^2-4x)+(3x-2)`

`=2x(3x-2)+(3x-2)`

`=(2x-1)(3x-2)`