Factoring polynomial through grouping

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SUMMARY

The discussion focuses on factoring the polynomial expression 2n - 6m + 5n^2 - 15mn through grouping. The user attempts to group the terms into pairs, identifying the greatest common factors (GCF) as 2 for the first pair (2n - 6m) and 5n for the second pair (5n^2 - 15mn). The user expresses confusion about the next steps after factoring, particularly regarding the treatment of exponents and maintaining the integrity of the expression. The correct factored form is 5n(n - 3m) + 2(n - 3m), leading to the final expression (n - 3m)(5n + 2).

PREREQUISITES
  • Understanding of polynomial expressions
  • Knowledge of factoring techniques, specifically grouping
  • Familiarity with greatest common factor (GCF) identification
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study polynomial factoring techniques, focusing on grouping methods
  • Practice identifying and applying the greatest common factor (GCF) in various expressions
  • Learn about the properties of exponents in algebraic expressions
  • Explore additional factoring methods, such as factoring by grouping and using the distributive property
USEFUL FOR

Students learning algebra, educators teaching polynomial factoring, and anyone seeking to improve their skills in algebraic manipulation and problem-solving.

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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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