How do you factor #6x²+4x-2#?
You have the factorization
To factor a trinomial, you simply have to look for its roots. There are three possible cases:
- The trinomial has no solutions. Then, it is not possible to factor it.
- The trinomial has only one solution
#x_0#. Then, it is a square of a binomial, more precisely, it is #a(x-x_0)^2#.
- The trinomial has two different solutions
#x_1#and #x_2#. Then, you can factor is as the product of two binomials, i.e. #a(x-x_1)(x-x_2)#.
The quantity that tells us how many solutions a trinomial has is its discriminant: if the trinomial is
In your case,
Your trinomial has two solutions, which are given by the formula
The two possible choices given by the