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welshfella

  • one year ago

I guess i've done problems like this in the past but I'm struggling with this one:- The polynomial Q(x) leaves remainder 4 when divided by x - 1, and remainder 8 when divided by x + 1. The remainder when Q(x) is divided by x^2 - 1 is A 32 B -4x + 9 C -4x - 7

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  1. welshfella
    • one year ago
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    obviously Q(1) = 4 and Q(-1) = 8 by the remainder theorem

  2. sohailiftikhar
    • one year ago
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    find the two values of x

  3. sohailiftikhar
    • one year ago
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    x^2-1=(x-1)(x+1) so x=1 and x=-1 put one by one in equation

  4. sohailiftikhar
    • one year ago
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    so the reminder is 32

  5. welshfella
    • one year ago
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    I dont follow that...

  6. sohailiftikhar
    • one year ago
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    as given in data reminder for (x-1)=4 and for (x+1)=8 so for x^2-1=(x-1)(x+1)=4*8=32

  7. sohailiftikhar
    • one year ago
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    now get it ?

  8. welshfella
    • one year ago
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    I don't think that's correct.

  9. welshfella
    • one year ago
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    I'd dont think this is particularly different - I'm just missing something

  10. geerky42
    • one year ago
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    *

  11. sohailiftikhar
    • one year ago
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    O.o so what you think huh ? It is correct bro

  12. sohailiftikhar
    • one year ago
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    so you just confused get calm and think on it for a minute

  13. welshfella
    • one year ago
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    I dont' know - but I don't think your logic is correct

  14. welshfella
    • one year ago
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    I'm going to look up the answer . I am confused - you are right there!! lol

  15. welshfella
    • one year ago
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    its -4x + 9

  16. sohailiftikhar
    • one year ago
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    yea! go an look the answer perhaps then you will believe on my answer

  17. sohailiftikhar
    • one year ago
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    no way it can't be

  18. sohailiftikhar
    • one year ago
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    take a screen short

  19. welshfella
    • one year ago
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    I'm helping my grandson with his maths revision. Well that's the answer in the book.

  20. welshfella
    • one year ago
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    I haven't got a scanner

  21. sohailiftikhar
    • one year ago
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    it's very simple .. ok tell me how they get 4 when they divide equation by (x-1) huh ?

  22. sohailiftikhar
    • one year ago
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    ok ganesh is here he can justify better now

  23. welshfella
    • one year ago
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    4 is the remainder and = q(1)

  24. ganeshie8
    • one year ago
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    Firstly, notice that we get a polynomial as remainder that is one degree less than whatever we're dividing by

  25. Nnesha
    • one year ago
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    ^

  26. welshfella
    • one year ago
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    right

  27. ganeshie8
    • one year ago
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    for example, (x^5+2x+1)/(x^2-1) gives a remainder that looks like \(ax+b\) yes ?

  28. welshfella
    • one year ago
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    right

  29. ganeshie8
    • one year ago
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    similarly (x^100 + x+1)/(x^10 + 1) gives a remainder that looks like \(ax^9+bx^8+\cdots\)

  30. ganeshie8
    • one year ago
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    the degree of remainder is always one less than the degree of bottom

  31. welshfella
    • one year ago
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    so the remainder in this case must be of the form ax + b?

  32. ganeshie8
    • one year ago
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    right, so lets suppose \[Q(x) = F(x)*(x^2-1)+\color{red}{ax+b}\] our goal is to find that red part

  33. welshfella
    • one year ago
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    ok

  34. ganeshie8
    • one year ago
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    since we know that \(Q(1)=4\) and \(Q(-1)=8\), plug them in and get two equations

  35. sohailiftikhar
    • one year ago
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    ganesh what you said about the given that reminder of that equation is 4 when divided by (x-1) where is x term with 4 ?

  36. ganeshie8
    • one year ago
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    \[Q(1) = F(1)*(1^2-1)+\color{red}{a*1+b} \implies 4 = \color{red}{a+b} \tag{1}\] \[Q(-1) = F(-1)*((-1)^2-1)+\color{red}{a(-1)+b} \implies 8 = \color{red}{-a+b} \tag{2}\] two equations and two unknowns, we can solve them

  37. ganeshie8
    • one year ago
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    for that, we may think that the coefficient of x is 0 @sohailiftikhar

  38. welshfella
    • one year ago
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    thats really clever Thanx ganesh

  39. ganeshie8
    • one year ago
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    np, im getting the remainder is \(-2x+6\) looks the options are wrong

  40. welshfella
    • one year ago
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    yes i got that too b = 6 ans a = -2

  41. welshfella
    • one year ago
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    I'll just recheck the answer in the book

  42. sohailiftikhar
    • one year ago
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    lol

  43. welshfella
    • one year ago
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    Yes thats the answer in the book. Well mistakes are made

  44. ganeshie8
    • one year ago
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    happens... our method is pretty robust and straightforward, nothing that could go wrong..

  45. sohailiftikhar
    • one year ago
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    from which grades book u got that problem bro ?

  46. welshfella
    • one year ago
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    Oh its a pretty old UK Advanced Level book from 1979. Examinations have become a little easier since then. Its wriiten by a professor of Mathematics but mistakes are made by everyone...

  47. sohailiftikhar
    • one year ago
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    lol ok

  48. welshfella
    • one year ago
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    Open study is a great place to study . There is a wealth a talent here.

  49. welshfella
    • one year ago
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    * wealth of talent

  50. sohailiftikhar
    • one year ago
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    yes:)

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