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Math Help - Factoring Trinomials

  1. #1
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    Factoring Trinomials

    My problem states to factor completely:

    49c+56c+16

    Nothing can be factored out as it is. So I took the product of 49 & 16 = 784 and two integers whose products equal 784 and sum equals 56 is (28)(28)

    Yet when I go to factor, it's not adding up. Maybe I am confusing the steps?

    49c2+28c+28c+16

    28c(c+21c) ?

    I am not sure what I am suppose to do actually...
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  2. #2
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    Re: Factoring Trinomials

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  3. #3
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    Re: Factoring Trinomials

    Factoring Trinomials-perfsq.jpg
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  4. #4
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    Re: Factoring Trinomials

    Hello, Kibbygirl!

    Factor completely: . 49c^2+56c+16

    Nothing can be factored out as it is.
    So I took the product of 49 & 16 = 784
    . . and two integers whose products equal 784 and sum equals 56 is (28)(28).

    Yet when I go to factor, it's not adding up. Maybe I am confusing the steps?

    49c^2+28c+28c+16 . This is correct!

    28c(c+21c) ? .But what is this?

    You are supposed to "factor by grouping".
    Are you familiar with it?

    You have: . 49c^2 + 28c + 28c + 16

    Factor the terms "by pairs".
    . . You can factor 7c from the first two terms
    . . You can factor 4 from the last two terms.

    Then you have: . 7c(7c+4) + 4(7c+4)

    Note that the term groups have (7c+4) on common . . . factor it out!

    And we have: . (7c+4)(7c+4) \:=\:(7c-4)^2


    See how it works?

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  5. #5
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    Re: Factoring Trinomials

    Thank you! I didn't realize I should be factor by grouping, I was trying to do the form x2+bx+c. I am vaguely familiar with factoring by grouping, so thank you for the steps.
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  6. #6
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    Re: Factoring Trinomials

    Soroban, can you tell me why in your final it is - and not +? Everything I am seeing in my book shows it'd be (7c+4)2??
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  7. #7
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    Re: Factoring Trinomials

    Quote Originally Posted by Kibbygirl View Post
    Soroban, can you tell me why in your final it is - and not +? Everything I am seeing in my book shows it'd be (7c+4)2??
    That was just a typo.
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  8. #8
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    Re: Factoring Trinomials

    Ok great, just wanted to verify in case I am not understanding correctly.
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