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Math Help - fastest way to factor quadratic

  1. #1
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    fastest way to factor quadratic

    What is the fastest possible way to factor a quadratic? Can someone explain to me how to use the guess and check method, and any limitations it may have (e.g. coefficient in front of x^2 must be 1)

    For example how would someone factor:
    6x^2+23x+20
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  2. #2
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    factoered from must be

    (ax+b)(cx+d) where a,b,c,d \in \Re

    in your example 6x^2+23x+20

    a\times c = 6 and b\times c = 20

    now starting guessing and checking:

    1) a=2, b= -4, c=3, d= -5 so (2x-4)(3x-5) now expand and check.

    keep guessing until you get the correct answer. Your example has many combinations to try, good luck...
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  3. #3
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    Another thing to think about is the signs. If you take a quadratic ax^2 \pm bx \pm c, where a is positive...

    If the quadratic as two plus signs, then the factored binomials both have plus signs:
    ax^2\;{\color{red}+}\;bx\;{\color{red}+}\;c = (?\;{\color{red}+}\;?)(?\;{\color{red}+}\;?)

    If the quadratic as a plus sign followed by a minus sign, then the factored binomials both have minus signs:
    ax^2\;{\color{red}-}\;bx\;{\color{red}+}\;c = (?\;{\color{red}-}\;?)(?\;{\color{red}-}\;?)

    Otherwise, the factored binomials will have one plus sign and one minus sign:
    ax^2\;{\color{red}+}\;bx\;{\color{red}-}\;c = (?\;{\color{red}+}\;?)(?\;{\color{red}-}\;?)
    OR
    ax^2\;{\color{red}-}\;bx\;{\color{red}+}\;c = (?\;{\color{red}+}\;?)(?\;{\color{red}-}\;?)

    Remembering this may cut down the number of guess-and-checks you have to try when factoring.


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