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Math Help - Remainder theorem

  1. #1
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    Remainder theorem

    Hi all,

    I have the fraction:

    (x^4 + 3x^2 - 4)/(x^2 + 1)

    We have been asked to express in mixed number form using i) long division and ii) using the remainder theorem.

    Have done the long division bit and got a remainder of -6.
    I am not sure how to use the remainder theorem with the x^2 + 1 as if you use f(-1) you get the remainder 0. How do i go about using the remainder theorem with a squared x?

    Thanks!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by steve@thecostins.co.uk View Post
    Hi all,

    I have the fraction:

    (x^4 + 3x^2 - 4)/(x^2 + 1)

    We have been asked to express in mixed number form using i) long division and ii) using the remainder theorem.

    Have done the long division bit and got a remainder of -6.
    I am not sure how to use the remainder theorem with the x^2 + 1 as if you use f(-1) you get the remainder 0. How do i go about using the remainder theorem with a squared x?

    Thanks!
    Technically you can't use x^2 + 1 with synthetic division. However if you set y = x^2 then your problem becomes to divide y^2 + 3y - 4 by y + 1 which can be done by synthetic division.

    -Dan
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  3. #3
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    Remainder theorem

    Thanks! I remember doing things like that before. But usually you have to work with y when you've finished.
    Do i have to do anything to y when i'm done? Otherwise they might has well just asked me work out the quadratic divided by x + 1.

    Does that make any sense?

    Many thanks
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