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Math Help - Factoring Quadratic Equations -- Splitting the Middle Term

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    Newbie happyface's Avatar
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    Question Factoring Quadratic Equations -- Splitting the Middle Term

    Is there a good way to always know how to split the middle term of a quadratic equation like x^2-9x+20=0?

    It turns out that -5x and -4x "works" but is there a better way to split the term that is less tedious?
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    Re: Factoring Quadratic Equations -- Splitting the Middle Term

    Quote Originally Posted by happyface View Post
    Is there a good way to always know how to split the middle term of a quadratic equation like x^2-9x+20=0?
    It turns out that -5x and -4x "works" but is there a better way to split the term that is less tedious?
    Note that the constant term is +, that means the two factors must have the same sign. But it must be - because the middle term is negative. So what are they?
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    Newbie happyface's Avatar
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    Re: Factoring Quadratic Equations -- Splitting the Middle Term

    Quote Originally Posted by Plato View Post
    Note that the constant term is +, that means the two factors must have the same sign. But it must be - because the middle term is negative. So what are they?
    I see! Negative 4 and 5 equal 9 when added, and 20 when multiplied.

    There are a few cases (like ax^2 + bx + c) where it is not so obvious where to split the middle term. That is especially where I get stumped, since c does not always equal the product of the "split" term.

    Thats actually what I meant to ask about.
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    Re: Factoring Quadratic Equations -- Splitting the Middle Term

    Quote Originally Posted by happyface View Post
    I see! Negative 4 and 5 equal 9 when added, and 20 when multiplied. There are a few cases (like ax^2 + bx + c) where it is not so obvious where to split the middle term. That is especially where I get stumped, since c does not always equal the product of the "split" term.
    BUT \frac{c}{a} is the product and -\frac{b}{a} is the sum.
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    Newbie happyface's Avatar
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    Re: Factoring Quadratic Equations -- Splitting the Middle Term

    Thanks! Very helpful.
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