SOLUTION: Factor 8w*2 - 14w + 3 I get 8w*2 - 12w - 2w + 3 then 4w(2w - 3) - (2w + 3) I even understand making it -1 but I am having a hard time understanding how (2w + 3) becomes (

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor 8w*2 - 14w + 3 I get 8w*2 - 12w - 2w + 3 then 4w(2w - 3) - (2w + 3) I even understand making it -1 but I am having a hard time understanding how (2w + 3) becomes (      Log On


   

Question 319121: Factor
8w*2 - 14w + 3
I get
8w*2 - 12w - 2w + 3
then
4w(2w - 3) - (2w + 3) I even understand making it -1 but I am having a hard time understanding how (2w + 3) becomes (2w - 3) as the answer would be (4w-1)(2w-3)
Thanks in advance!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
8w%5E2-14w%2B3=%28aw-b%29%28cw-d%29
.
.
.
When you multiply the right hand side (FOIL method), you get,
%28aw%2Bb%29%28cw%2Bd%29=acw%5E2%2Badw%2Bbcw%2Bbd
%28aw-b%29%28cw-d%29=%28ac%29w%5E2%2B%28ad%2Bbc%29w%2Bbd
So you need to choose integers a,b,c,d so that,
ac=8
ad%2Bbc=-14
bd=3
.
.
.
As you have seen, when b=-1, d=-3, then
bd=3
-3a-c=-14
which can be solved with
a=4 and b=2
Since ab=8 so,
8w%5E2-14w%2B3=%284w-1%29%282w-3%29
.
.
.
Best way to become proficient in this reverse FOIL method is to work plenty of forward FOIL problems to start to see the connections between the coefficients in the polynomials and the factors.
Then the reverse process won't seem so daunting.