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Math Help - polynomial functions help

  1. #1
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    polynomial functions help

    i received an assignment and i am unsure of where to start.
    the question i cant solve is this:

    Given p(x) = x^3 - x + 1, find all values of a such that p (a - 1) > p(1)
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  2. #2
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    Quote Originally Posted by plasticfang View Post
    Given p(x) = x^3 - x + 1, find all values of a such that p (a - 1) > p(1)
    First expand:
    p\left( {a - 1} \right) = \left( {a - 1} \right)^3  - \left( {a - 1} \right) + 1 = a^3  - 3a^2  + 2a + 1
    Now solve a^3  - 3a^2  + 2a + 1 > 1 = p(1) for a.
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  3. #3
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    am i doing the right thing if i go
    a(a^2 - 3a + 2) > 0
    a(a - 1)(a - 2) > 0
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  4. #4
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    Quote Originally Posted by plasticfang View Post
    am i doing the right thing if i go
    a(a^2 - 3a + 2) > 0
    a(a - 1)(a - 2) > 0
    YES! You have it!
    Why don't you finish it off?
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  5. #5
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    ok just got back from work.

    so my a values would be 0 1 and 2?
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