Factoring polynomial through grouping

AI Thread Summary
The discussion focuses on factoring the polynomial 2n - 6m + 5n^2 - 15mn through grouping. The initial grouping separates the terms into 2(n - 3m) and 5n(n - 3m), with the goal of finding a common factor. There is confusion regarding the treatment of exponents during the factoring process. Participants emphasize the importance of accuracy in maintaining letters and operation signs while factoring. The conversation highlights the need for careful step-by-step execution in polynomial factoring.
DPXJube
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Homework Statement


2n - 6m + 5n^2 - 15mn


Homework Equations


No particular equation since this is factoring


The Attempt at a Solution


Keep in mind that I struggle when it comes to grouping as I'm not sure where I'm supposed to start but...

2n - 6m + 5n^2 - 15mn
Group first 2 terms together
2n - 6m
GCF is 2. Factor into...
2(n-3n)
Group last 2 terms together
5n^2 - 15mn
GCF is 5n. Factor into
5n(n - 3m) (For this part I'm not too sure what happens to the exponent. I assume me dividing 5n^2 by 5n turned it into a 1)
Now I have
2(n+3)5n(n - 3m)

From this point on I have no idea what to do.
Help would be much appreciated.
 
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You've made a number of very sloppy errors. Do it again slowly and be sure not to change letters and operation signs.
 

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