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Math Help - 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 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 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 a and c values together. You need to find two numbers that multiply to become ac and add to become b.

    To use the examples on that page...

    2x^2 + 13x - 7.

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

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


    2x^2 + 13x - 7 = 2x^2 + 14x - 1x - 7

     = 2x(x + 7) - 1(x + 7)

     = (x + 7)(2x - 1).


    The second example...

    6x^2 - 19x + 3.

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

    Break up the middle term into -18x - 1x...

    6x^2 - 19x + 3 = 6x^2 - 18x - 1x + 3

     = 6x(x - 3) - 1(x - 3)

     = (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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