Question

Factor the trinomial. You many need to check the discriminant to make sure it can be factored. SHOW YOUR WORK.

Answer 1

Check the discriminant (always a good idea).

b^2 - 4ac 
b = -19
c = -15
a = 10

(-19)^2 - 4(10)(-15)
361 + 600
961

Yes it can be factored, but if you like, you could use the quadratic formula.
x = [- (-19) +/- sqrt(961)]/(2 * 10)
x = [19 +/- 31 ] / 20
x = (19 + 31/20
x = (50)/20
x = 5/2

x = [19 - 31] / 20
x = [- 12]/20
x = -3/5

Getting the factors is a little tricky.
(x - 5/2)(x + 3/5) = 0
The first factor is found by putting 
x - 5/2 in that form and multiplying through by 2
1/2 (2x - 5) The 1/2 comes from multiplying by 2. 

The second factor is
1/5 (5x + 3)

So the equation will look like 
1/2(2x - 5)1/5(5x + 3) = 0 If you multiply by 2 you get
(2x - 5)1/5(5x + 3) = 0 and now multiply by 5 you get
(2x - 5) (5x + 3) 

Check
2x*5x - 25x + 6x - 15
10x^2 - 19x - 15 = 0

So everything works out.