How do you factor 5y2 - 2y - 3?

Answer 1

(5y + 3)(y - 1)

You can get this because you know that the only factors of 5 are 5 and 1, so you start

(5y )(y )

Then, to multiply two things to get -3, it has to be -3 and 1, or -1 and 3. Guessing and checking works from here, or you can think it out. 5 x -1 would give you -5, and 3 x 1 is 3, so this combination would give you the -2 coefficient needed to get the answer. FOIL to check.