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Math Help - Factoring

  1. #1
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    Exclamation Factoring

    Pretty sure factoring would be in the algebra department... hoping so. Anyways, can anyone help me factor this equation?

    3x^2-10x+3

    I can't seem to figure it out.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Factoring

    Try solving for roots using the quadratic equations. I got  x_1 = 3, x_2 = \frac{1}{3}

    so (x-3)(x-\frac{1}{3}) = x^2 - \frac{1}{3}x - 3x + 1 = 0
    multiply left hand side by 3 to remove fraction so  3*(x-\frac{1}{3})(x-3)  = (3x-1)(x-3) = 3x^2-10x + 3
    Last edited by jakncoke; February 7th 2013 at 04:16 PM.
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  3. #3
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    Re: Factoring

    Okay, this makes sense! For some reason I couldn't find the solution.. lol. Thank you so much!
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  4. #4
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    Re: Factoring

    In such cases first multiply the coefficient of x^2 and constant term. In this case that is 3 *3 = 9. Find such factors of this product such that their sum equals the coefficient of x. In this question we get 9 = -1 * -9 and -1 + ( -9) = -10
    Rewrite the quadratic by splitting the middle term.
    3x^2 - x - 9x + 3 = x ( 3x - 1) - 3 ( 3x - 1 ) = (3x-1)(x-1) and there after it is quite simple.
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  5. #5
    Newbie pssingh1001's Avatar
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    Re: Factoring

    3x^2-10x+3=0
    the quadratic eq^n satisfies with x=3
    then x-3=0
    then we can write
    i.e 3x^2-9x-x+3=0
    3x(x-3) -1 (x-3)=0
    i.e (x-3)(3x-1)=0
    then we can write
    x-3=0 & 3x-1=0
    then x=3 & x=1/3
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