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Math Help - Is there a better way to factor this trinomial?

  1. #1
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    Is there a better way to factor this trinomial?

    My time is pretty limited when I take tests and quizzes, and this problem seems like it would take too long for what its worth given my current knowledge.

    36y^2-35+12y

    i can get 36y^2+42y-30y-35 and do the rest from there. However I am wondering if theres a quicker way to figure this problem out. The way I get this is:

    36*-35=-1260
    42*-30 = -1260
    42+-30= 12

    I dont know how im supposed to just know that or calculate that in a reasonable amount of time. so im wondering is there some trick to factoring trinomials like this in a faster, more efficient way? I typically use the grouping method. Hopefully my only options arent limited to pure trial and error.
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  2. #2
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    Quote Originally Posted by NecroWinter View Post
    My time is pretty limited when I take tests and quizzes, and this problem seems like it would take too long for what its worth given my current knowledge.

    36y^2-35+12y

    i can get 36y^2+42y-30y-35 and do the rest from there. However I am wondering if theres a quicker way to figure this problem out. The way I get this is:

    36*-35=-1260
    42*-30 = -1260
    42+-30= 12

    I dont know how im supposed to just know that or calculate that in a reasonable amount of time. so im wondering is there some trick to factoring trinomials like this in a faster, more efficient way? I typically use the grouping method. Hopefully my only options arent limited to pure trial and error.
    You could try simplifying as follows...

    36y^2+12y-35=(6y)^2+2(6y)+7(-5)=(6y+7)(6y-5)
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    You could try simplifying as follows...

    36y^2+12y-35=(6y)^2+2(6y)+7(-5)=(6y+7)(6y-5)
    Why dont they just show it that way initially? Jeez. Thats so much simpler. Thank you.
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  4. #4
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    True.
    We don't see the word "substitution" mentioned often when factoring these...

    x=6y

    36y^2+12y-35=(6y)(6y)+2(6y)-35=x^2+2x-35

    Now we need the factors of -35 to combine and give us 2 (the coefficient of x).

    (x+a)(x+b)=x^2+2x-35\Rightarrow\ a+b=2,\;\;ab=-35

    The numbers are 7,\;\;-5
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