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.

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- Apr 17th 2012, 06:56 AMCapnzimsFactoring 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. - Apr 17th 2012, 07:11 AMbiffboyRe: 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. - Apr 17th 2012, 09:33 AMCapnzimsRe: 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. - Apr 17th 2012, 10:24 AMmastersRe: Factoring by grouping help
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!

- Apr 17th 2012, 10:26 AMbiffboyRe: 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. - Apr 17th 2012, 10:59 AMCapnzimsRe: Factoring by grouping help
So by me factoring out the -5 i change the signs inside the parenthesis?

That helps a ton thanks! - Apr 17th 2012, 11:57 AMCapnzimsRe: 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? - Apr 17th 2012, 09:55 PMbiffboyRe: 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