11/28/12 how do we factor by grouping ?

How do we factor by grouping ?

- When you factor your taking out common terms so you need to group them , for example :
x^3+3x^2-4x-12
First factor the first half of the equation : x^3+3x^2
this becomes : x^2(x+3) because you take out the common factor and make it so that if you foil it you get what the original half of the equation was.
Second ,now you do the same thing to the other half of the equation: 4x-12
this becomes 4(x+3) because four can come out of each term
Third , you can now combine like terms (x^2 +4) (x+3)
but one of the terms can be simplified still so;
 The final equation becomes (x+2)(x+2)(x+3)