The trinomial is 8x^2 + 15x - 2.
Its discriminant is d = = = 289.
Its roots are (use the quadratic formula)
= = = .
= = = ;
= = = -2.
THEREFORE, the factoring is
8x^2 + 15x - 2 = = = (8x-1)*(x+2). ANSWER
(Note: I would guess that "factor the trinomial" means perform the factoring. Finding the roots using the quadratic formula and using the roots to do the factoring -- as the other tutor did -- is probably not what was wanted from the student....)
Here is one of a number of different ways you can do this factoring.
(1) Multiply the leading coefficient (8) times the constant term (-2) to get -16.
(2) Find two numbers whose product is -16 and whose sum is the coefficient of the middle term, 15. Those numbers are 16 and -1 (16 times -1 is -16; 16 plus -1 is 15).
(3) Use those two numbers to break the middle term 15x into two terms 16x and -1x and factor by grouping.
