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Math Help - Factoring by grouping help

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    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.
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  4. #4
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    Re: Factoring by grouping help

    Quote Originally Posted by Capnzims View Post
    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,

    12x^3+2x^2-30x-5 =

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

    2x^2(6x+1)-5(6x+1) =

    (2x^2-5)(6x+1)

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

    -5(6x+1)=-30x-5

    See!
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  5. #5
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    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.
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  6. #6
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    Re: Factoring by grouping help

    So by me factoring out the -5 i change the signs inside the parenthesis?
    That helps a ton thanks!
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  7. #7
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    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?
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  8. #8
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    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
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