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Can someone please explain this for me?? C3 Algebraic fractions - Remainder Theorem

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    (Original post by BrianBlack)
    Must be true then.
    LoL

    I find that students often find C3 the hardest ... it does introduce a number of new topics that C4 then expands on ... for good mathematicians certainly C4 seems to be the easier of the 2
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    (Original post by TenOfThem)
    LoL

    I find that students often find C3 the hardest ... it does introduce a number of new topics that C4 then expands on ... for good mathematicians certainly C4 seems to be the easier of the 2
    I would say the jump from C2 to C3 is the challenge for some. Personally I feel topics like applications of differential equations, paramertic integration and some vectors work is on paper potentially more challenging but by the time they get there they have matured.
    Same from GCSE to C1 and then finding C2 easier I think.
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    Sorry for the bump but I thought I would agree with the OP, the book really doesn't explain this well at all. It has taken me hours to get my head around this but it finally makes sense. It's strange that there are literally no youtube videos on this exact type of question.
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    (Original post by Crowbar)
    Sorry for the bump but I thought I would agree with the OP, the book really doesn't explain this well at all. It has taken me hours to get my head around this but it finally makes sense. It's strange that there are literally no youtube videos on this exact type of question.
    I will have to disagree with you here. I also used the book to learn C3 and i did find that the book explanation is very good.

    I really don't understand how can such a simple concept take hours, on which part did you got stuck.

    First we have to make up an equation with some constant and then use the technique learned in year 8 of comparing coefficients
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    I didn't get where the constants were supposed to go when dividing by different denominators like x squared. Lack of different examples I suppose.
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    (Original post by Crowbar)
    I didn't get where the constants were supposed to go when dividing by different denominators like x squared. Lack of different examples I suppose.
    There are exercises in the book, the solutions of them are available so can't you use them as examples as well.

    This is probably the easiest topic of C3, so i can't completely understand how can an A-Level student struggle on this.
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    (Original post by Mr M)
    I think TenOfThem has already done this but here it is again.

    From the question:

    x^3 + x^2 - 7 = (Ax^2 + Bx + C)(x-3) + D

    Expand the brackets and collect like terms:

    x^3 + x^2 - 7 = Ax^3 + (B-3A)x^2 + (C-3B)x + D - 3C

    Now just look at the x^3 terms:

    x^3 = Ax^3

    Clearly A = 1

    Now look at the x^2 terms

    x^2 = (B-3A)x^2

    This means B = 4.

    Now look at the x terms (there is no x term on the left hand side):

    0 = (C-3B)x

    C = 12

    Finally match up the constants:

    -7=D-3C

    D = 29
    Just wanted to say thank you for this explanation. I was having some trouble with the remainder theorem and this was a big help. I looked through all sorts of books and resources and didn't understand, but your explanation was brilliant. The commentary especially helped me soak it in.
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    (Original post by .Rapid.)
    Just wanted to say thank you for this explanation. I was having some trouble with the remainder theorem and this was a big help. I looked through all sorts of books and resources and didn't understand, but your explanation was brilliant. The commentary especially helped me soak it in.
    :thumbsup:
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    (Original post by Mr M)
    :thumbsup:
    Not quite as good as this explanation, though:

    (Original post by Mr M)
    A giant crocodile ate the rest.
    :rofl:
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    (Original post by Brit_Miller)
    Not quite as good as this explanation, though:



    :rofl:
    I'm usually so patient too.
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    (Original post by Mr M)
    I'm usually so patient too.
    I honestly thought he was just trying to wind you two up at first!
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    (Original post by Brit_Miller)
    I honestly thought he was just trying to wind you two up at first!
    we will never know :rolleyes:
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    (Original post by Brit_Miller)
    I honestly thought he was just trying to wind you two up at first!
    She not he.

    I don't think so, if someone struggles on such things then i am not surprised if she struggles on the thread related stuff.
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    (Original post by TenOfThem)
    we will never know :rolleyes:

    Haha, inspired effort, though. I feel sorry for the wall you must've been banging your head against.
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    (Original post by Brit_Miller)
    Haha, inspired effort, though. I feel sorry for the wall you must've been banging your head against.
    Patience is a virtue

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    Use Synthetic division.

    The stupid equating method sucks and also takes alot of time.
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    (Original post by Zenarthra)

    The stupid equating method sucks and also takes alot of time.
    No it doesn't
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    (Original post by Zenarthra)
    The stupid equating method sucks and also takes alot of time.
    I did it in my head in less than 20 seconds so the evidence suggests otherwise.
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    (Original post by Mr M)
    I did it in my head in less than 20 seconds so the evidence suggests otherwise.
    boff
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    (Original post by TenOfThem)
    Did post 5, 6, and 7 not help at all then
    You helped me <3

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Updated: November 10, 2012
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