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Math Help - Factoring Quadratic Equations

  1. #1
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    Factoring Quadratic Equations

    Can i get some help these are the last 5 problems that im stuck with. -_-

    (COMPLETED)1) (X-Y)^3 +27

    (COMPLETED)2) X^2-A^2+X-A

    (COMPLETED)3) 3x^(-3/2) - 12x^(1/2)

    4) x^(1/2) (x-4)^(-1/2) +3x^(-1/2) (x-4)^(-3/2)

    (COMPLETED)5) x^(2n+2) +x^(n+2)-56x^2


    for 3 im think its (3x^-3/2)(1-4x^2) but yeah im not sure. but everything else im clueless at right now. thxs for hte help!
    Last edited by Nismo; November 17th 2009 at 09:09 PM.
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  2. #2
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    1) 27 = 3^3, difference of two cubes.

    2) If you factorize (difference of two squares) the two first terms, you get (x - a)(x + a) + (x - a). Can you see the common factor ?

    Now I have no time for the other ones, sorry. I did 40% of the job though !
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  3. #3
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    Quote Originally Posted by Nismo View Post
    ...

    3) 3x^(-3/2) - 12x^(1/2)

    ...

    for 3 im think its (3x^-3/2)(1-4x^2) but yeah im not sure. but everything else im clueless at right now. thxs for hte help!
    1. Your result is OK but unfinished:

    2. When factoring out a term from a sum you have to divide each summand by the factor. In your case:

    3x^{-\frac32} - 12x^{\frac12} = 3x^{-\frac32} \left(\dfrac{3x^{-\frac32}}{3x^{-\frac32}} - \dfrac{12x^{\frac12}}{3x^{-\frac32}} \right) = 3x^{-\frac32}\left(1-4x^2\right)

    3. The sum in the bracket is a difference of squares which can be factorized immediately. Therefore the result is:

    3x^{-\frac32} - 12x^{\frac12} = 3x^{-\frac32}(1-2x)(1+2x)
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  4. #4
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    thxs earboth i just noticed that i didnt factor it all the way out -_- it was like 12ish i think when i was doing this.. -_-



    also for that 1st problem i was getting

    ((x-y)-3)(x^2-2xy+y^2+3x-3y+9) but it looks wrong. is it?


    and for 2 i actually did factor out to that

    but didnt know where to go from thier. i thought it would be somthing like

    (x-a)((1+1)(1-1))-1 but i dont think its that.
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  5. #5
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    1. a^3+b^3= (a+b)(a^2-ab+b^2)
    you need to leave (x-y) intact and not multiply it out.


    5. Take out a factor of x^2 and then it may look familiar.

    Quote Originally Posted by Nismo View Post
    and for 2 i actually did factor out to that

    but didnt know where to go from thier. i thought it would be somthing like

    (x-a)((1+1)(1-1))-1 but i dont think its that.
    take out (x-a)

    (x-a)(x+a)+(x-a)=(x-a)((x+a)+1)
    Last edited by Krahl; November 15th 2009 at 05:49 PM.
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  6. #6
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    Quote Originally Posted by Krahl View Post
    1. a^3+b^3= (a+b)(a^2-ab+b^2)
    you need to leave (x-y) intact and not multiply it out.


    5. Take out a factor of x^2 and then it may look familiar.



    take out (x-a)

    (x-a)(x+a)+(x-a)=(x-a)((x+a)+1)

    i see how you did it, and that it does distribute out to the x^2-y^2+x-a but im still getting marked wrong on it o_0

    wouldnt it just be (x-a)(x+a+1) without the prenthesis in side?
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  7. #7
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    not sure about #4. this is what i am up to

    \frac{(x - 3)(x - 1)}{\sqrt{x^2 - 4x}(x - 4)}
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  8. #8
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    Quote Originally Posted by Nismo View Post
    i see how you did it, and that it does distribute out to the x^2-y^2+x-a but im still getting marked wrong on it o_0

    wouldnt it just be (x-a)(x+a+1) without the prenthesis in side?
    If your doing one of them online things then sometimes extra brackets do effect answers. try it without the brackets see what it says
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  9. #9
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    naw found out my teacher did his coding wrong. and he said it was right! thxs for the help! although i still gotta finish the rest of the problems!! ha.
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  10. #10
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    5. Take out a factor of x^2 and then it may look familiar.

    x^(2n+2) +x^(n+2)-56x^2= x^2x^{2n}+x^2x^n-56x^2
    =x^2(x^{2n}+x^n-56)=x^2((x^n)^2+x^n-56)

    can you factorise the stuff in the brackets?
    hint y^2+y-56=(y+8)(y-7)
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  11. #11
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    Quote Originally Posted by Krahl View Post
    5. Take out a factor of x^2 and then it may look familiar.

    x^(2n+2) +x^(n+2)-56x^2= x^2x^{2n}+x^2x^n-56x^2
    =x^2(x^{2n}+x^n-56)=x^2((x^n)^2+x^n-56)

    can you factorise the stuff in the brackets?
    hint y^2+y-56=(y+8)(y-7)

    haha i actually got that far last night with the x^2((x^n)^2+x^n-56) but i didnt know how to factor it out from thier although i knew it had to deal with 7 and 8. but yeah i got it fianlly! thxs!
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