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Math Help - Polynomial long division

  1. #1
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    Polynomial long division

    I've been trying to get my head around the method that my lecturer uses, it's not the regular one we used in secondary school, and it's not synthetic division. You put the larger of the two on the left and the smaller on the right, and then figure out what the smaller is multiplied by to get the larger + remainder.
    So for example to divide x^4-x^3+x-1 by x^4-x^3+x-1 you would do:

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

    Then take x^3-x^2+x-1 to the next line and divide by the remainder (-x^2+2x-1)

    I understand it for small ones like that, but when it's larger ones like x^10 or where the coefficient of x isn't 1 I can't do them...
    Please help!
    Thanks
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  2. #2
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    Quote Originally Posted by silverblue22 View Post
    I've been trying to get my head around the method that my lecturer uses, it's not the regular one we used in secondary school, and it's not synthetic division. You put the larger of the two on the left and the smaller on the right, and then figure out what the smaller is multiplied by to get the larger + remainder.
    So for example to divide x^4-x^3+x-1 by x^4-x^3+x-1 you would do:
    What? x^4- x^3+ x- 1 divided by x^4- x^3+ x- 1 is "1" by inspection.

    x^4-x^3+x-1= (x^3-x^2+x-1)(x)-x^2+2x-1[/quote]
    No, you wouldn't. Or, at least, I wouldn't. If I hadn't noticed that the divisor and dividend are exactly the same, I would think, looking at the highest powers just as in dividing numbers you look at the first few digits to get an estimate of a quotient. x^4 divides into x^4 once so the "quotient" is 1, then we subtract 1(x^4- x^4+ x- 1) from x^4- x^3+ x- 1 and see that my remainder is 0. Problem finished!

    Then take x^3- x^2+ x- 1 to the next line and divide by the remainder (-x^2+2x-1).

    I understand it for small ones like that, but when it's larger ones like x^10 or where the coefficient of x isn't 1 I can't do them...
    Please help!
    Thanks
    No, you don't understand it. You never "divide by the remainder".
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  3. #3
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    Oops, can't believe I got the question wrong!

    It was meant to be divide x^4-x^3+x-1 by x^3-x^2+x-1

    So you go x^4-x^3+x-1= (x^3-x^2+x-1)(x)-x^2+2x-1

    Then bring x^3-x^2+x-1 to the left, let it = the remainder from the last line
    (-x^2+2x-1)(-x-1)+2x-2

    Then -x^2+2x-1= (2x-2)(-x/2+1/2)

    Anyone recognise this method at all?
    Thanks for your reply... even if I did get it completely wring in the first place
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