How do you factor 6a^2 + 17ab + 12b^2

Answer 1

You just have to guess-and-check for factoring. (After guessing, FOIL to make sure that it works out.) Typically, the numbers will be the closest factors of the number. For example, 12 = 4*3. (Those are the closest factors.) 6 = 3*2. (Those are the closest factors.) Here you go...
(3a+4b)(2a+3b)