Question

How do you factor the trinomial `3x²+5x-2`?

Answer 1

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

Explanation:

It is easy to check that the expression vanishes for `x=-2` - which means that `x+2` is a factor. We can exploit this to rewrite the expression in the following manner :

`3x^2+5x-2 =3x^2+6x-x-2 = 3x(x+2)-1(x+2) = (3x-1)(x+2)`