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Math Help - Help Me Factor Please

  1. #1
    soca615
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    Exclamation Help Me Factor Please

    I really need some help factoring some equations please. These don't neccessarily have to be in the real numbers either so

    1.) 4x^4 + 3x^2 - 1
    2.) 9c^4 + 5c^2 + 1
    3.) x^3 + x^2 + 4
    4.) (a+b)^2 + 7(a+b) + 12
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by soca615
    I really need some help factoring some equations please. These don't neccessarily have to be in the real numbers either so

    1.) 4x^4 + 3x^2 - 1
    2.) 9c^4 + 5c^2 + 1
    3.) x^3 + x^2 + 4
    4.) (a+b)^2 + 7(a+b) + 12
    Hello,

    to factorize those expressions use the the rule of Vieta:

    to 1) 4x^4+3x^2-1=(2x-1)(2x+1)(x^2+1)
    to 2)  9c^4 + 5c^2 + 1=\left(c^2+\frac{1}{9} \right) \left(c^2+1 \right)
    to 3) x^3 + x^2 + 4=(x+2)(x^2-x+2)
    to 4)  (a+b)^2 + 7(a+b) + 12=((a+b)+3)((a+b)+4)

    Bye
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by earboth
    to 2)  9c^4 + 5c^2 + 1=\left(c^2+\frac{1}{9} \right) \left(c^2+1 \right)
    2) Isn't correct, sorry.
    9c^4 + 5c^2 + 1 doesn't factor over the reals. The way I would approach this, then would be to set 9c^4 + 5c^2 + 1 = 0. The solution is c^2= -5/18 \pm \sqrt{-11}/18, so 9c^4 + 5c^2 + 1
     = 9(c^2+5/18 + \sqrt{-11}/18)(c^2+5/18 - \sqrt{-11}/18), or you can take the square root of c^2 (i.e. solve for c, not c^2) and string the four factors together. Don't forget the extra 9!

    -Dan
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