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Thread: Null factor Law

  1. #1
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    Null factor Law

    Factorise and solve:

    x^2 + 6x - 72 = 0
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  2. #2
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    this is a relatively easy factorization...

    (x+12)(x-6)=0

    x=-12, 6

    Why did you have a problem with it?
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  3. #3
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    Smile

    Just wasn't thinking right. Though don't get me wrong, usually I am not that good at math also. So, I'm prone to mistakes.
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  4. #4
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    Here is the whole process so you can study it

    $\displaystyle x^2+6x-72=0$

    We try find the factos adding to 6

    $\displaystyle 1(-72)=-72$ $\displaystyle -71$
    $\displaystyle 2(-36)=-72$ $\displaystyle -34$
    $\displaystyle 3(-24)=-72$ $\displaystyle -21$
    $\displaystyle 4(-18)=-72$ $\displaystyle -14$
    $\displaystyle 6(-12)=-72$ $\displaystyle -6$
    $\displaystyle 12(-6)=-72$ $\displaystyle 6$

    Now we have to re-write our equation

    $\displaystyle x^2+12x-6x-72=0$
    $\displaystyle x(x+12)-6(x+12)=0$
    $\displaystyle (x-6)(x+12)=0$

    Then:
    $\displaystyle x-6=0$
    $\displaystyle x=6$

    or
    $\displaystyle x+12=0$
    $\displaystyle x=-12$
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