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anonymous

  • one year ago

Factor x^3-5x^2-25x+125

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  1. anonymous
    • one year ago
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    5x(x^2-x-5+25)

  2. welshfella
    • one year ago
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    - no - thats gives 5x^3

  3. welshfella
    • one year ago
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    x+ 5 or x-5 might be a factor find f(5) and see if it = 0

  4. anonymous
    • one year ago
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    So (x+5)(x-5)(x-5)

  5. anonymous
    • one year ago
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    What type of roots of those?

  6. Michele_Laino
    • one year ago
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    we can factor out x^2 between the first two terms, and we can factor out -25x between the third and the fourth term, so we get this: \[\Large {x^3} - 5{x^2} - 25x + 125 = {x^2}\left( {x - 5} \right) - 25x\left( {x - 5} \right)\]

  7. welshfella
    • one year ago
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    OOOH - did you guess that?? (x-5) is a factor because f(5) = 0

  8. anonymous
    • one year ago
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    No. I just did (x^2-25)(x-5)

  9. welshfella
    • one year ago
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    well you are correct

  10. anonymous
    • one year ago
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    What type of roots are those?

  11. anonymous
    • one year ago
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    And thanks youu

  12. Michele_Laino
    • one year ago
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    oops... we can factor out 25 between the third and the fourth terms, not 25 x: \[\Large {x^3} - 5{x^2} - 25x + 125 = {x^2}\left( {x - 5} \right) - 25\left( {x - 5} \right)\]

  13. welshfella
    • one year ago
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    right

  14. welshfella
    • one year ago
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    - you beat me too it!!

  15. anonymous
    • one year ago
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    So would the roots be -5,-5,5 or -5,5,5?

  16. welshfella
    • one year ago
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    the roots are 5 and -5 root 5 is a duplicate

  17. anonymous
    • one year ago
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    Ok but since the polynomial is 3 there has to be 3 roots?

  18. welshfella
    • one year ago
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    - correction - that was rubbish the roots are 5 , 5 and -5

  19. anonymous
    • one year ago
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    How?

  20. welshfella
    • one year ago
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    yes -5 and 5 duplicity 2

  21. welshfella
    • one year ago
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    factors are (x + 5)(x - 5)(x - 5) the fist gives x = -5 and the other 2 give x = 5

  22. anonymous
    • one year ago
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    Ohhh<3

  23. anonymous
    • one year ago
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    Thanks! :)

  24. welshfella
    • one year ago
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    no 3 roots - because there are 2 5's

  25. welshfella
    • one year ago
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    the graph will look a bit like |dw:1436970554356:dw|

  26. welshfella
    • one year ago
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    - just touching the point (5,0)

  27. anonymous
    • one year ago
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    :) Thank you!!

  28. welshfella
    • one year ago
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    yw

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