How does one go about factoring

2(3m+1)^2-7(3m+1)-15(3m+1)

Please show me how to solve this.

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- Sep 12th 2010, 12:40 PMGerardFactoring
How does one go about factoring

2(3m+1)^2-7(3m+1)-15(3m+1)

Please show me how to solve this. - Sep 12th 2010, 12:44 PMe^(i*pi)
- Sep 12th 2010, 12:53 PMGerard
I did that but the answer on the sheet I was given is

While if I do it how you would I get

- Sep 12th 2010, 12:58 PMe^(i*pi)
is also a factor of both terms so that can be taken out too

- Sep 12th 2010, 01:02 PMGerard
OHHH everything seems to have clicked in my head now thank you.

- Sep 12th 2010, 01:37 PMHallsofIvy
The first thing I see is that there is a "3m+1" in each term. Taking that out leaves (3m+1)(2(3m+1)- 7- 15). Now you can combine -7- 15= -22 as e^(i*pi) suggests as well as multipy out 2(3m+1) to get (3m+ 1)(6m+ 2- 22)= (3m+1)(6m- 20). If you really want to you could observe that both 6m and 20 are divisible by 2 so you can factor a little further: 2(3m+1)(3m- 10)