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Math Help - Factor the expression

  1. #1
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    Factor the expression

    can somone solve this for me so i can figure out how to do the rest i got to do my teacher used some X method to solve it she put at the bottom the middle number the multiplied the first and last and put it at the top of the x

    4xto the 2nd power-5x-6
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  2. #2
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    I can't decipher how this equation is supposed to appear.

    4x^2-5x-6 Like this?

    (4x\pm\alpha)(x\pm\beta)

    \alpha * \beta =-6

    4x*\beta + x*\alpha = -5x
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  3. #3
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    yup
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  4. #4
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    Quote Originally Posted by dwsmith View Post
    I can't decipher how this equation is supposed to appear.

    4x^2-5x-6 Like this?

    (4x\pm\alpha)(x\pm\beta)

    \alpha * \beta =-6

    4x*\beta + x*\alpha = -5x
    Could also be (2x\pm\alpha)(2x\pm\beta) ?
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  5. #5
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    I used a CAS system to check it. It isn't 2x.
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  6. #6
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    Fair call, I hadn't gone that far!
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  7. #7
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    Quote Originally Posted by shadower4 View Post
    can somone solve this for me so i can figure out how to do the rest i got to do my teacher used some X method to solve it she put at the bottom the middle number the multiplied the first and last and put it at the top of the x

    4xto the 2nd power-5x-6
    \displaystyle 4x^2 - 5x - 6.

    Multiply your \displaystyle a and \displaystyle c values to give \displaystyle 4(-6) = -24.

    This means you need to find two numbers that multiply to give \displaystyle -24 and add to give \displaystyle -5.

    They are \displaystyle -8 and \displaystyle 3.

    So you split the middle term \displaystyle -5x into \displaystyle -8x + 3x.



    \displaystyle 4x^2 - 5x - 6 = 4x^2 - 8x + 3x - 6

    \displaystyle = 4x(x - 2) + 3(x - 2)

    \displaystyle = (x - 2)(4x + 3).
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