Hi Lizzy,

The first step in solving this equation is to factor the quadratic 3x² + x - 2. The only factors of 3 are 3 and 1 so, if this quadratic can be factored then the factorization will be

(3x      )(x      )

where there are two terms missing. These two missing terms must multiply together to give the constant term -2. Thus the two missing terms are plus or minus 2 and plus or minus 1. Thus, if a factorization exists it must be one of

(3x + 2)(x  - 1)
(3x - 2)(x + 1)
(3x + 1)(x - 2) or
(3x - 1)(x + 2)

Expand each one and see if you get a middle term of x.

Penny