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Math Help - polynomial division

  1. #1
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    polynomial division

    the expression
    f(x) = x^3 + ax^2 + bx + 10
    is divisible by (x+2) but leaves a remainder of 12 when divided by (x+1)

    a) Find the values of a and b
    b) solve the equation f(x) = 0

    i have done a) (i think) and come up with a = 4 b = -7 (is that right)

    and im completely stumped on b)

    any help is appericated
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  2. #2
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    I get a=-4\;\&\;b=-7
    Now you know that (x+2) is one factor so x=-2 is one root.
    Use that to find the other roots.
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  3. #3
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    thank you

    so x = -2, x = + 1 and x = + 5

    just so i can see where i went wrong how did you geta = -4

    thanks again
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  4. #4
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    If a given polynomial expression f is divided by x-a, then the remainder is the number f(a).

    Because the expression is divisible by (x+2), it has a remainder of 0.

    Use these facts to solve for a and b.
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  5. #5
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    Quote Originally Posted by Chop Suey View Post
    If a given polynomial expression f is divided by x-a, then the remainder is the number f(a).
    I just want to clarify that a in that instance is just an arbitrary number and not the one related to the question.
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