Question 15507
Factoring trinomials can entail a lot of educated guess-and-check work.

Factor:

{{{15x^2 - x - 2}}}  What are the possible factors of the {{{x^2}}} term?

1) (15x)(x) or (-15x)(-x)
2) (5x)(3x) or (-5x)(-3x)

What are the possible factors of the constant term?

1) (1)(-2) or (-1)(2)

What combintation will give the x-term coefficient of -1?

1) (3)(-2) + (5)(1) This looks promising!
2) (-3)(2) + (5)(1) This won't do because you need to get a -2 as a constant term.

So, try:

{{{(5x - 2)(3x + 1)}}} Check it out using FOIL.

{{{(5x - 2)(3x + 1) = 15x^2 + 5x - 6x - 2}}} = {{{15x^2 -x -2}}}