Thread: Factoring

How does one go about factoring

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

Please show me how to solve this.

Originally Posted by Gerard

How does one go about factoring

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

Please show me how to solve this.

You may combine the last two terms, just like



You now need to find the highest common factor of both terms. One factor is 2 because both 2 and 22 are divisible by 2

I did that but the answer on the sheet I was given is



While if I do it how you would I get

is also a factor of both terms so that can be taken out too

OHHH everything seems to have clicked in my head now thank you.

Originally Posted by Gerard

How does one go about factoring

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

Please show me how to solve this.

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)