Question 144219
3x^2 - 19x - 40
:
First write it:
(3x ___)(x ___)
: 
You know the values in the blanks will be factors of -40, 
(one will be neg, the other positive):
1, 40
2, 20
4, 10
5, 8
Because the middle term is neg, the larger factor has to be negative
:
FOIL these values until you get the given expression:
:
(3x + 5)(x - 8) FOILs to 3x^2 - 24x + 5x - 40 which is:
:
3x^2 - 19x - 40
FOIL these values until the 
:
:
factor: 9x^2 - 12x + 4 
:
The clue on this one is that both the coefficient of x (9) and 4 are perfect squares.
Try these values first. 
:
Since the middle term is neg and the 3rd terms is positive it must be:
(3x - 2)(3x - 2)  or (3x-2)^2
:
FOIL this and you get the original expression:
9x^2 - 6x - 6x + 4 = 9x^2 - 12x + 4
:
Practice doing these and it will become pretty easy.