Me. i've been stuck all day! i need to factor 10x^2-19x-51

10X^2 + 15x-34x -51
5x (2x+3)-17(2x+3)
(5x-17) (2x+3)

Well, you first need to look at what goes into 10 and 51.

10:
1*10 = 10
2*5 = 10
not a lot of numbers.

51:
1*51
3*17
not a lot of numbers either.

now, very rarely is it 1 * (whatever the number, so in this case let's use 51.)

We need both numbers from x to multiply to be 10.
The only logical one here is 5*2

So far:
(5x ? ?) (2x ? ?)

Your best safe bet to do for your next one is to not use the 1*57, but the 17*3.

So, now:
(5x ? 17) (2x ? 3)
You need both to be a negative ( negative times a negative is a positive), so...

Your
(5x - 17) (2x + 3)