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Question 430895: x^2 +3x-40 over x^2+2x-35 divided by x^2 +2x-48 over x^2+3x-18
I reached the correct factor pairs of (x-3)(x+6) over (x+7)(x-6) after I had done the required canceling.
The book reached the same factors pairs yet coming in the following order: (x+6)(x-3) over (x+7) (x-6)
When I took a test for my current Math 102 distance education course I found that order of the pairs did matter in factoring and that is why I am concerned my pairs didn't come out the way the book has them stated. If you could take a moment to look at my factoring that I list below as an example I would appreciate it. Please let me know how I can come out with the correct factor pair ORDER that the book has. Thank you for your time for looking at this.
My example of factoring x^2+3x-4, the first thing listed in the rational expression I have stated above:
for x^2+3x-40 my order was (x 5)(x 8) --note: I fill in the signs later. . .anyhow, I reached this order because when I used a subtraction shortcut to see if my Outer and Inner of the FOIL came to my middle term my subtraction problem read----8-5=+3 since I started with the Outer first and then finished with the inner of the foil so my final factor pair for this first one was
(x-5)(x+8)my other factor pair that came under the (x-5)(x+8)was (x-5)(x+7)the other part of the rational expression after I flipped it since it was division was (x-3)(x+6) over (x-6)(x+8)
thank you again for the time you took to look at this.please forgive the long explanation,I just wanted to be clear,but I understand if you think it is just too long to bother with.
Sincerely,
Elisa
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! Step back a second and think back to the commutative rules.
Does a*b = b*a ??
You know it does.
So if a = (x-3) and b=(x+6)
does it matter which factor is listed first?
Nope
So your answer and the book's answer are mathematically equivalent.
Not sure where you found that order of factor matters. Order does not matter when mulitplying.
Here's a nice tool to help verify your factoring work --> http://72.3.253.76:8080/webMathematica3/quickmath/algebra/factor/basic.jsp
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