# Thread: Factoring by grouping help

1. ## Factoring by grouping help

I dont understand factoring by grouping could someone help me using this problem with step by step instructions please

12^p3-21^p2+28p-49

Thanks for any help. I really wanna grasp this.

2. ## Re: Factoring by grouping help

I think you mean 12p^3-21p^2+28p-49

In which case I can see a factor 3p^2 in the 1st two terms and a factor 7 in the last two terms

So it becomes 3p^2(4p-7)+7(4p-7)

I can now see (4p-7) in both parts so I 'lift' it out and get (4p-7)(3p^2+7)

You can check that these two brackets multiply out to the original question.

3. ## Re: Factoring by grouping help

Thank you very much. That gives me a much firmer understanding of how to do this. I do have another question related to his. In this problem.

12x^3 + 2x^2 -30x-5 the answer is (2x^2-5)(6x+1)
My question on this is: the GCF of -30x and -5 is: 5 or is it -5?
Second question: and how do they become positive during the factoring
ex. 2x^2(6x+1) - 5(6x-1) see what I'm saying sorry trying to explain it the best I can. How does the 6x-1 end up being 6x+1.

4. ## Re: Factoring by grouping help

Originally Posted by Capnzims
Thank you very much. That gives me a much firmer understanding of how to do this. I do have another question related to his. In this problem.

12x^3 + 2x^2 -30x-5 the answer is (2x^2-5)(6x+1)
My question on this is: the GCF of -30x and -5 is: 5 or is it -5?
Second question: and how do they become positive during the factoring
ex. 2x^2(6x+1) - 5(6x-1) see what I'm saying sorry trying to explain it the best I can. How does the 6x-1 end up being 6x+1.
Hi Capnzims,

$\displaystyle 12x^3+2x^2-30x-5 =$

$\displaystyle (12x^3+2x^2)+(-30x-5)=$

$\displaystyle 2x^2(6x+1)-5(6x+1) =$

$\displaystyle (2x^2-5)(6x+1)$

When you factored out a $\displaystyle -5$ from the last 2 terms, you had to change the signs of each term inside. Distribute back to verify:

$\displaystyle -5(6x+1)=-30x-5$

See!

5. ## Re: Factoring by grouping help

If you remove the last bracket you've written we get -30x+5. We want -30x-5 which is what we will get if we have 6x+1 in the bracket

Lifting (6x+1) out of both parts gives us the answer.

6. ## Re: Factoring by grouping help

So by me factoring out the -5 i change the signs inside the parenthesis?
That helps a ton thanks!

7. ## Re: Factoring by grouping help

Another question same situation.
4v^3-12v^2-5v+15
in the middle of factoring i get
4v^2(v-3) -5v+15
then I do this
4v^2(v-3)-5(v-3)
when i did that part im switching both symbols of -5v+15 right when i factor out the -5?

8. ## Re: Factoring by grouping help

See if this helps. When you 'factor out' -5 the other factor will be (-5v+15) divided by -5

That is -5v/-5+15/-5=v-3