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Math Help - factorise

  1. #1
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    factorise

    hi,

    i nned to factorise this:

    3x^2+5x-2=0

    i know how to do these but im stuck on this one!

    so if someone could lend some advise i would be very grateful!

    thanks!
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  2. #2
    MHF Contributor harish21's Avatar
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    5x = 6x-x

    So,

    3x^2+5x-2

    =3x^2+6x-x-2
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  3. #3
    MHF Contributor harish21's Avatar
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    Last edited by harish21; March 18th 2011 at 08:22 AM. Reason: accidental double post.
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  4. #4
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    i don't understand, wouldn't you have 2 brackets one starting with 3x and the other x.
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by andyboy179 View Post
    i don't understand, wouldn't you have 2 brackets one starting with 3x and the other x.
    Hi andyboy,

    You are correct, but harish21 was showing you a neat little way of factoring besides the "guess and check" method.

    Here is harish21's method.

    First, multiply the leading coefficient times the constant: 3 times -2 = -6

    Next, determine two numbers whose product is -6 and whose sum is the coefficient of the linear term which is +5.

    You should easily see that -1 and 6 meet that criteria.

    Replace 5x in your original quadratic expression to 6x - 1x.

    3x^2+6x-1x-2

    Group the first two terms and factor out 3x.

    3x(x+2)-1x-2

    Group the last two terms and factor out -1.

    3x(x+2)-1(x+2)

    It's easy to see the two binomial factors are (x+2)(3x-1)

    It takes a lot longer to explain it than it does to actually do it.
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