Factoring polynomial through grouping

In summary, the expression 2n - 6m + 5n^2 - 15mn can be factored into 2(n-3m)(n+3). However, there were some errors made in the process of factoring, such as incorrectly grouping the terms and changing operation signs. It would be helpful to review the steps of factoring and practice carefully to avoid making these errors.
  • #1
DPXJube
12
0

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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  • #2
You've made a number of very sloppy errors. Do it again slowly and be sure not to change letters and operation signs.
 

1. What is factoring polynomial through grouping?

Factoring polynomial through grouping is a method used to simplify a polynomial expression by rearranging and grouping terms that have common factors.

2. Why is factoring polynomial through grouping useful?

Factoring polynomial through grouping can help us to easily solve and graph polynomial equations, as well as find the roots or zeros of a polynomial function.

3. How do you factor polynomial through grouping?

To factor polynomial through grouping, we first group together terms that have a common factor. Then, we use the distributive property to factor out the common factor from each group. Finally, we can simplify the expression by factoring out any remaining common factors.

4. What are the common mistakes to avoid when factoring polynomial through grouping?

Common mistakes when factoring polynomial through grouping include not properly grouping terms, forgetting to factor out a common factor, and incorrectly simplifying the expression. It is important to double check your work and make sure all terms are accounted for.

5. Can all polynomial expressions be factored through grouping?

No, not all polynomial expressions can be factored through grouping. This method only works if the polynomial has terms that have common factors. If there are no common factors, then we would need to use other factoring methods, such as the quadratic formula or completing the square.

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