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Math Help - Polynomials Divison and remainder

  1. #1
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    Question Polynomials Divison and remainder

    I have don't understand how to solve problems like this:
    When we divide f(x) by (x-1), (x-2) and (x+1) the remainders are 3, 7 and 5. Find the remainder of f(x) divided by (x-1)(x-2)(x+1).

    I try to write them like this:
    f(x) = P*(x-1)+3
    f(x) = Q*(x-2)+7
    f(x) = R*(x+1)+5
    To get a result like this after some manipulation:
    f(x) = S*(x-1)*(x-2)*(x+1)+y
    But I can't.
    Help me please.
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  2. #2
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    The first thing you should note, from the remainder theorem, is that

    f(1) = 3, f(2) = 7, f(-1) = 5.

    Are you told what degree the polynomial is?
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  3. #3
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    Quote Originally Posted by Prove It View Post
    The first thing you should note, from the remainder theorem, is that

    f(1) = 3, f(2) = 7, f(-1) = 5.

    Are you told what degree the polynomial is?
    No, That is the complete problem.
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