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.
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.
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!