Homework Help

Please Factor using Quadratic Expressions. State whether it haus a common factor and...

user profile pic

paulbarton | Honors

Posted October 18, 2012 at 11:52 PM via web

dislike 1 like

Please Factor using Quadratic Expressions. State whether it haus a common factor and pattern. Use decomposition and show step by step. 

5. B. 6m^2+13mn+2n^2

 

 

Tagged with decomposition, factoring., math

1 Answer | Add Yours

user profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted October 19, 2012 at 12:51 AM (Answer #1)

dislike 1 like

If you have more than one question, you need to make separate posts.

To factor using decomposition, you need to find factors of the product of the first and last coefficient that sum to the middle coefficient.  

In this case, you are looking for factors of 6x2=12 that sum to 13.  This gives factors of 12 and 1.

Then split the middle term up using these coefficients.  Finally, use factoring by grouping on the resulting expression twice.

For this expression, we get:

`6m^2+13mn+2n^2`   split middle term using factors 12 and 1

`=6m^2+12mn+mn+2n^2`   factor by grouping

`=6m(m+2n)+n(m+2n)`   factor again 

`=(m+2n)(6m+n)`

The expression factors to `(m+2n)(6m+n)` .

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes