SOLUTION: This is for Introductory Algebra (College). Instructions are to FACTOR BY GROUPING. My instructor said to "arbitrarily change a positive to a negative if necessary to get the cor

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This is for Introductory Algebra (College). Instructions are to FACTOR BY GROUPING. My instructor said to "arbitrarily change a positive to a negative if necessary to get the cor      Log On


   

Question 107867: This is for Introductory Algebra (College). Instructions are to FACTOR BY GROUPING. My instructor said to "arbitrarily change a positive to a negative if necessary to get the correct answer". That just doesn't make sense to me. I have a tendency to over-think things and I really want to know why and how I get to the correct answer. Is it really possible to just randomly make things up in math?????
I will show my work. Thank you in advance for any help you can give as you will likely be keeping me out of a straight-jacket at this point!
original problem to be factored by grouping:
p^2-2p-3rp+6r
my work:
(p^2-2p)-1(3rp+6r)
(p^2-2p)+(-3rp-6r)
p(p-2) -3r(p+2) OR p(p-2) +3r(-p-2) (THIS IS WHERE IT GOES DOWNHILL!!)
(?????)(p-3r) ... Final Answer is SUPPOSED to be (p-2)(p-3r)
Obviously I will never get that as an answer at the rate I am going.
Again, thank you for any possible help.


Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
You are right; there are options at times but
not arbitraries.
========================
Your problem:
original problem to be factored by grouping:
p^2-2p-3rp+6r
original problem to be factored by grouping:
p^2-2p-3rp+6r
p(p-2) -3r(p-2)
(p-2)(p-3r)
==============
Cheers,
Stan

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
p%5E2-2p-3rp%2B6r Start with the given expression


p%5E2-2p%2B-3rp%2B6r Rewrite -3rp as + -3rp. Remember adding a negative is the same as subtracting


%28p%5E2-2p%29%2B%28-3rp%2B6r%29 Group like terms


p%28p-2%29%2B%28-3rp%2B6r%29 Factor out the GCF p out of the first group


p%28p-2%29-3r%28p-2%29 Factor out the GCF -3r out of the second group


Notice how we have a common factor of p-2, so we can now combine like terms


%28p-3r%29%28p-2%29 Combine like terms


Notice how %28p-3r%29%28p-2%29 foils back to p%5E2-2p-3rp%2B6r. So this verifies our answer


note: you made an error on your second step. When you factor out a negative 1 you should get %28p%5E2-2p%29-1%283rp-6r%29 not %28p%5E2-2p%29-1%283rp%2B6r%29.