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Math Help - Factoring quadratics

  1. #1
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    Factoring quadratics

    For example:
    <br />
6x^2 +11x -35<br />

    I've been doing this by trial and error but it takes too long. I tried googling "factoring quadratics" but when it comes to examples like this, they just use the quadratic equation to find the values of x assuming the whole equation was equal to zero in the first place. I don't think this helps me.

    I need the answer in the form (....)(....) and I don't think the answer on, for example,
    Solving Quadratic Equations: Examples, does that
    . What I need is the strategy to find this. I know I'm going to need +7. -5 or -7, +5 at the ends but from there I just have to try so many combinations.
    Last edited by TYTY; March 24th 2009 at 04:15 AM.
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  2. #2
    MHF Contributor
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    Talking

    Try this lesson on factoring quadratics.

    (The posted link was for solving equations, rather than factoring expressions.)
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  3. #3
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    Quote Originally Posted by stapel View Post
    Try this lesson on factoring quadratics.

    (The posted link was for solving equations, rather than factoring expressions.)
    yes this looks exactly like what I am looking for
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  4. #4
    Member rtblue's Avatar
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    There is a quadratic formula, to find the roots. Google Quadratic formula. I personally prefer factoring tho
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by TYTY View Post
    For example:
    6x2 + 11x 35

    I've been doing this by trial and error but it takes too long. I tried googling "factoring quadratics" but when it comes to examples like this, they just use the quadratic equation to find the values of x assuming the whole equation was equal to zero in the first place. I don't think this helps me.

    I need the answer in the form (....)(....) and I don't think the answer on, for example, Solving Quadratic Equations: Examples, does that. What I need is the strategy to find this. I know I'm going to need +7. -5 or -7, +5 at the ends but from there I just have to try so many combinations.
    Hi TYTY,

    Here's one strategy you might find helpful.

    6x^2+11x-35

    Multiply the leading coefficient (6) by your constant (-35) to get -210.


    Next, try to come up with 2 factors that multiply to get -210 and sum to +11.

    You may have to fiddle around a little to find them, but this one came to me right away. It's +21 and -10.

    Replace the middle coefficient (-11) with these two numbers:

    6x^2+21x-10x-35

    Now, group the first two terms and the last 2 terms and factor out the greatest common factor for each.

    3x(2x+7)-5(2x+7)

    Use the distributive property to finish up.

    (3x-5)(2x+7)
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  6. #6
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    Quote Originally Posted by masters View Post
    Hi TYTY,

    Here's one strategy you might find helpful.

    6x^2+11x-35

    Multiply the leading coefficient (6) by your constant (-35) to get -210.


    Next, try to come up with 2 factors that multiply to get -210 and sum to +11.

    You may have to fiddle around a little to find them, but this one came to me right away. It's +21 and -10.

    Replace the middle coefficient (-11) with these two numbers:

    6x^2+21x-10x-35

    Now, group the first two terms and the last 2 terms and factor out the greatest common factor for each.

    3x(2x+7)-5(2x+7)

    Use the distributive property to finish up.

    (3x-5)(2x+7)
    Excellent explanation.
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