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Thread: Tips on factoring, a not equal to 1

  1. #1
    Mar 2008

    Tips on factoring, a not equal to 1

    Hi everyone!

    I am going in for a job interview in the math lab at school and in the interview I'm going to be asked about 7-10 questions from these areas:

    Basic Arithmetic
    Intro/Intermediate Algebra
    College Algebra
    Calculus I

    The thing I'm really concerned about that I always end up slipping on factoring trinomials when the leading coefficient is not 1.

    I remember my algebra teacher taught me a way that you could multiply together the leading coefficient and the constant term, then find factors of that and do something with those factors....does anyone know what I'm talking about?

    Let's take for example the trinomial $\displaystyle 6x^2+11x+3$

    Does anyone know what method I'm referring to..or if you have an easier way with some more examples...any help is much appreciated!

    My interview is on Tuesday by the way, and I'm going to be practicing problems like crazy! If anyone wants to throw some more basic problems at me from the subjects I listed above, feel free to; I need all the practice I can get!

    PS: mods, feel free to move this thread if you think it would be better in another area!
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  2. #2
    o_O is offline
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    o_O's Avatar
    Mar 2008
    For the general $\displaystyle ax^{2} + bx + c$, I find two factors such that they multiply to $\displaystyle ac$ and add up to $\displaystyle b$.

    For your example: $\displaystyle 6x^{2} + 11x + 3$

    Find two factors that multiply to (6)(3) = 18 and that add up to 11. 9 and 2 should come up.

    Now, split 11x into 9x + 2x (that's where your factors come in):
    $\displaystyle 6x^{2} + 11x + 3 = \underbrace{6x^{2} {\color{blue}+ 2x} }_{\text{Factor}} {\color{blue} +} \underbrace{{\color{blue} 9x} + 3}_{\text{Factor}}$
    $\displaystyle = 2x{\color{red}(3x+ 1)} + 3{\color{red}(3x+ 1)}$
    $\displaystyle = {\color{red}(3x+ 1)}(2x + 3)$

    This should always work (assuming that your quadratic is factorable).
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  3. #3
    Mar 2008

    That's the trick..I don't know why I have such a hard time remembering that! It is now forever sealed in my memory..I will be practicing..

    Thank you o_O!
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