Expert: Chen Min - 4/2/2008

Question
Factor completely
1.)  u^2-5uv+6v^2
2.)  9x^2-23x-12
Is there any way you could also explain to me how to solve the problem or show me step by step?

Answer
I believe this question does not fall into the A Math category...

Anyway, I'll help you out.

The way to factorise a quadratic polynomial usually involves a method called "cross multiply".

Consider an expression:
(Ax + By)(Cx + Dy),where A,B,C,D are constant integers.
Expand it, you get
ACx^2 + (AD + BC)xy + BDy^2.Don't tell me you don't know how to expand.

Then consider your first question
Replace x with u and y with v
Then you find that AC = 1, and BD = 6, as well as AD + BC = 5;
As A,C are integers, A and C must both be 1.(There is no need to take into account the negative here)
Thus D + B = 5
There goes natually that either B = 2,D = 3 or B = 3,D = 2
Hence u^2-5uv+6v^2 = (u + 2v)(u + 3v)

For the second one,treat y as 1

You'll understand and do it faster after many practices.Shortcut does not suit your,I perceive.

Hope this helps:)