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Math Help - polynomial help please

  1. #1
    Newbie
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    Mar 2008
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    polynomial help please

    I have to factor these polynomials
    64x^3+343
    400x^2-25
    x^4+8x^2-9
    2x^3-3x^2+4x-6
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  2. #2
    Senior Member Peritus's Avatar
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    <br />
\begin{gathered}<br />
  400x^2  - 25 = \left( {20x - 5} \right)\left( {20x + 5} \right) \hfill \\<br />
  2x^3  - 3x^2  + 4x - 6 = \left( {x - 1.5} \right)\left( {2x^2  + 4} \right) \hfill \\ <br />
\end{gathered} <br />
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  3. #3
    Super Member
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    London / Cambridge
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    first one use the sum of two cubes formula.

    a^3+b^3 = (a+b)(a^2-ab+b^2)

    it will be helpful to write 64x^3+343 <br />
as <br />
(4x)^3 + 7^3



    for the second one, use the difference of two squares formula a^2 - b^2 = (a-b)(a+b)

    it may be helpful to write 400x^2-25 <br />
as (20x)^2-5^2


    the third one, first factor by inspection.

    x^4+8x^2-9  = (x^2 -1)(x^2 +9)

    then use the difference of two squares formula on the first factor


    For the last one, are you familiar with synthetic division ? if i told you (2x-3) was a factor could you factor it ?
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  4. #4
    Newbie
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    =]

    thanks for the helppp!
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