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Math Help - Cubic Equation Problem

  1. #1
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    Cubic Equation Problem

    1) Let f(x) = x^3 - kx^2 +2kx - k - 1
    a) Show that f(x) is divisible by x-1, well thats obvious f(1) = 0
    but then there is part b - factorise it.
    I know how to do it when there is a number, but its confusing when there is a pronumeral, how do i go about this. Specifically the "long division" method.
    Also, any tips and hints for when you are solving a worded question?

    Cheers
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by theleontan View Post
    1) Let f(x) = x^3 - kx^2 +2kx - k - 1
    a) Show that f(x) is divisible by x-1, well thats obvious f(1) = 0
    but then there is part b - factorise it.
    I know how to do it when there is a number, but its confusing when there is a pronumeral, how do i go about this. Specifically the "long division" method.
    Also, any tips and hints for when you are solving a worded question?

    Cheers
    I can never make the code look good for something like long division, but there is always synthetic division.

    -Dan
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  3. #3
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    e^(i*pi)'s Avatar
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    Alternatively you can compare coefficients

    x^3-kx^2+2kx-(k+1) = (x-1)(Ax^2+Bx+C)


    To start you off you can say that: -C = -(k+1) \rightarrow C = (k+1). A is also simple to calculate using the same method
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