Expert: Richard J. Raridon - 11/19/2008

Question
Im 16 (jr). i am really bad at factoring, to the point were i just spent over 15 minutes trying to figure out how to factor out ((6d-9)/
(5d+1))/((6-13d+6d^2)/(15d^2-7d-2))
and i still havnt got it all done yet.
i dnt understand factoring, and do alot of it by quess checking, and revising (over and over and over)
Please help me try to figure out how to factor.

Answer
For (6d-9)  the only factoring is 3(2d-3)
For (6-13d+6d^2) you know that the factors are (w-xd) and (y-zd) where wy=6 and xz=6.  So w and y have to be 2&3 or 1&6, and the same for x and z.  You can see pretty quickly that 1&6 won't work and you end up with (3-2d) and (2-3d)
Similarly, for (15d^2-7d-2) you have (wd-x) and (yd-z) where
where xz =-2 and wy = 15 so w and y can be 1&15 or 3&5.  You just have to play around with them until you find the right combination, in this case (3d-2) and (5d+1)