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Thread: Quadratic Trinominals

  1. #1
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    Question Quadratic Trinominals

    Hey everyone, I know this is probably basic for you but I really can't understand this.

    This is the lesson I've been following.
    Factoring Quadratic Trinomials by MATHguide

    I have learned to Factorise the Quadratic Equations which is (Factoring $\displaystyle ax^2 + bx + c : a=1)$ on that website, I think thats pretty easy, But for some reason I really dont understand the next part which is (Factoring $\displaystyle ax^2 + bx + c : a>1$)

    I think I understand what it's trying to get to, but I just can't get my head around it.

    Does anyone have any easier or alternative ways of understanding this ?
    Thanks.
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  2. #2
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    There's an easier way. Multiply your $\displaystyle a$ and $\displaystyle c$ values together. You need to find two numbers that multiply to become $\displaystyle ac$ and add to become $\displaystyle b$.

    To use the examples on that page...

    $\displaystyle 2x^2 + 13x - 7$.

    Multiplying our $\displaystyle a$ and $\displaystyle c$ values gives $\displaystyle -14$. So we need two numbers that multiply to give $\displaystyle -14$ and add to be $\displaystyle 13$. They are $\displaystyle 14$ and $\displaystyle -1$.

    So we break up the middle value into $\displaystyle 14x - 1x$ and then factorise by grouping.


    $\displaystyle 2x^2 + 13x - 7 = 2x^2 + 14x - 1x - 7$

    $\displaystyle = 2x(x + 7) - 1(x + 7)$

    $\displaystyle = (x + 7)(2x - 1)$.


    The second example...

    $\displaystyle 6x^2 - 19x + 3$.

    Multiply the $\displaystyle a$ and $\displaystyle c$ values, we get $\displaystyle 18$. So we need two numbers that multiply to give $\displaystyle 18$ and add to $\displaystyle -19$. They are $\displaystyle -18$ and $\displaystyle -1$.

    Break up the middle term into $\displaystyle -18x - 1x$...

    $\displaystyle 6x^2 - 19x + 3 = 6x^2 - 18x - 1x + 3$

    $\displaystyle = 6x(x - 3) - 1(x - 3)$

    $\displaystyle = (x - 3)(6x - 1)$.


    Is this clearer now?
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  3. #3
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    Thank you so much!
    This is much clearer, I'll run through some more equations when I get home from work.
    This is much easier to understand thank you!
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