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Math Help - Solving Polynomial Expressions

  1. #1
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    Solving Polynomial Expressions

    If I can only get on a few problems I'll have an idea on how to complete the WS.... It's been driving me crazy...

    Factor the expression on the left side of each equation. Then solve the equation.

    4) 2x^3-250=0

    Factor it (I think) to: (2x)^3 ....then what? 250 can't be squared....

    Same directions...

    9) x^4-5x^2+4=0

    I have no idea what to do...

    Two more problems:

    Factor each expression.

    25) x^3-125

    Solve each equation:

    x^4-x=0

    If you could help at all, that'd be great. I tried looking for help online and in my book... and I can't find anything...
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  2. #2
    Junior Member
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    Oct 2008
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    4) divide across eqn by 2

    then difference of cubes is given by




    9) let y = x^2

    solve eqn for y

    then use y = x^2 to get x


    25) difference of two cubes again


    x^4-x = x(x^3-1)
    hope this helps!
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  3. #3
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    I'm still lost....
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  4. #4
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    4) 2x^3-250 = 0
    x^3 -125 = 0

    x^3 = 125
    x = 5 ( cube root of 125)

    9) let y = x^2

    then eqn becomes
    y^2 -5y +4 = 0

    (y-4)(y-1) = 0

    so y - 4 = 0 then y = 4 = x^2 so x = 2,-2
    or y -1 = 0 then y = 1 = x^2 so x = 1,-1

    25)

    x^4 - x = x(x^3-1) = 0

    so x = 0

    or x^3 - 1 = 0 ie x^3 = 1 so x = 1
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