I am so confused.

How do I factor:
35x^2 - 46x + 15

this one is not really easy. If there are any rational roots, they must be in the group of

±15 ±5 ±3 ±1
±3/5 ±1/5
±1/7 ±3/7 ±5/7 ±15/7
±1/35 ±3/35

That's a lot of guesswork. I guess I'd start in the middle, since 46 is a lot less than 35*15.

(7x-5)(5x-3) --> -46x HEY! got it in one!

Just dumb luck, though. I might have had to try a bunch of possibilities