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Math Help - Factoring Trinomials...I think?

  1. #1
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    Unhappy Factoring Trinomials...I think?

    Hello all. I've been working on this stuff all day...and I just thought to Google math forums, and ended up here! Well..there are a couple of problems that differ slightly from each other that I'm having problems with. The first one is...

    12x+34x+24

    I believe the first step is to find the GCF, which is 6, and divide.

    6x (2x+17+4)

    -sigh- This is as far as I get though...a little help would be so very much appreciated.
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  2. #2
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    Quote Originally Posted by burgessjkkb View Post

    I believe the first step is to find the GCF, which is 6, and divide.

    6x (2x+17+4)
    Correct, although you now have 6 (2x^2+17x+4) not 6x (2x+17+4) . The x term is not common to take out.

    To factor 2x^2+17x+4 look for a solution (trial and error) such that 2x^2+17x+4 = (2x+a)(x+b) where a and b multiply to give 4.

    This must also expand to give 17x as the middle term. Could take some time. Good luck!
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  3. #3
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    First of all, 6 \cdot 17 \neq 34.

    In fact, 6 does not go into 34.

    The highest common factor is actually 2.


    So 12x^2 + 34x + 24 = 2(6x^2 + 17x + 12).


    Now, instead of using trial and error, find two numbers that multiply to become 6 \cdot 12 = 72 and add to become 17.

    I think you'll find that the numbers are 9 and 8.


    So 2(6x^2 + 17x + 12) = 2(6x^2 + 9x + 8x + 12)

     = 2[3x(2x + 3) + 4(2x + 3)]

     = 2(2x + 3)(3x + 4).
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