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Thread: 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.

    $\displaystyle 4x^2-5x-6$ Like this?

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

    $\displaystyle \alpha * \beta =-6$

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

    $\displaystyle 4x^2-5x-6$ Like this?

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

    $\displaystyle \alpha * \beta =-6$

    $\displaystyle 4x*\beta + x*\alpha = -5x$
    Could also be $\displaystyle (2x\pm\alpha)(2x\pm\beta)$ ?
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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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    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
    $\displaystyle \displaystyle 4x^2 - 5x - 6$.

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

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

    They are $\displaystyle \displaystyle -8$ and $\displaystyle \displaystyle 3$.

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



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

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

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