welshfella
  • welshfella
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
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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welshfella
  • welshfella
obviously Q(1) = 4 and Q(-1) = 8 by the remainder theorem
sohailiftikhar
  • sohailiftikhar
find the two values of x
sohailiftikhar
  • sohailiftikhar
x^2-1=(x-1)(x+1) so x=1 and x=-1 put one by one in equation

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More answers

sohailiftikhar
  • sohailiftikhar
so the reminder is 32
welshfella
  • welshfella
I dont follow that...
sohailiftikhar
  • sohailiftikhar
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
sohailiftikhar
  • sohailiftikhar
now get it ?
welshfella
  • welshfella
I don't think that's correct.
welshfella
  • welshfella
I'd dont think this is particularly different - I'm just missing something
geerky42
  • geerky42
*
sohailiftikhar
  • sohailiftikhar
O.o so what you think huh ? It is correct bro
sohailiftikhar
  • sohailiftikhar
so you just confused get calm and think on it for a minute
welshfella
  • welshfella
I dont' know - but I don't think your logic is correct
welshfella
  • welshfella
I'm going to look up the answer . I am confused - you are right there!! lol
welshfella
  • welshfella
its -4x + 9
sohailiftikhar
  • sohailiftikhar
yea! go an look the answer perhaps then you will believe on my answer
sohailiftikhar
  • sohailiftikhar
no way it can't be
sohailiftikhar
  • sohailiftikhar
take a screen short
welshfella
  • welshfella
I'm helping my grandson with his maths revision. Well that's the answer in the book.
welshfella
  • welshfella
I haven't got a scanner
sohailiftikhar
  • sohailiftikhar
it's very simple .. ok tell me how they get 4 when they divide equation by (x-1) huh ?
sohailiftikhar
  • sohailiftikhar
ok ganesh is here he can justify better now
welshfella
  • welshfella
4 is the remainder and = q(1)
ganeshie8
  • ganeshie8
Firstly, notice that we get a polynomial as remainder that is one degree less than whatever we're dividing by
Nnesha
  • Nnesha
^
welshfella
  • welshfella
right
ganeshie8
  • ganeshie8
for example, (x^5+2x+1)/(x^2-1) gives a remainder that looks like \(ax+b\) yes ?
welshfella
  • welshfella
right
ganeshie8
  • ganeshie8
similarly (x^100 + x+1)/(x^10 + 1) gives a remainder that looks like \(ax^9+bx^8+\cdots\)
ganeshie8
  • ganeshie8
the degree of remainder is always one less than the degree of bottom
welshfella
  • welshfella
so the remainder in this case must be of the form ax + b?
ganeshie8
  • ganeshie8
right, so lets suppose \[Q(x) = F(x)*(x^2-1)+\color{red}{ax+b}\] our goal is to find that red part
welshfella
  • welshfella
ok
ganeshie8
  • ganeshie8
since we know that \(Q(1)=4\) and \(Q(-1)=8\), plug them in and get two equations
sohailiftikhar
  • sohailiftikhar
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 ?
ganeshie8
  • ganeshie8
\[Q(1) = F(1)*(1^2-1)+\color{red}{a*1+b} \implies 4 = \color{red}{a+b} \tag{1}\] \[Q(-1) = F(-1)*((-1)^2-1)+\color{red}{a(-1)+b} \implies 8 = \color{red}{-a+b} \tag{2}\] two equations and two unknowns, we can solve them
ganeshie8
  • ganeshie8
for that, we may think that the coefficient of x is 0 @sohailiftikhar
welshfella
  • welshfella
thats really clever Thanx ganesh
ganeshie8
  • ganeshie8
np, im getting the remainder is \(-2x+6\) looks the options are wrong
welshfella
  • welshfella
yes i got that too b = 6 ans a = -2
welshfella
  • welshfella
I'll just recheck the answer in the book
sohailiftikhar
  • sohailiftikhar
lol
welshfella
  • welshfella
Yes thats the answer in the book. Well mistakes are made
ganeshie8
  • ganeshie8
happens... our method is pretty robust and straightforward, nothing that could go wrong..
sohailiftikhar
  • sohailiftikhar
from which grades book u got that problem bro ?
welshfella
  • welshfella
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...
sohailiftikhar
  • sohailiftikhar
lol ok
welshfella
  • welshfella
Open study is a great place to study . There is a wealth a talent here.
welshfella
  • welshfella
* wealth of talent
sohailiftikhar
  • sohailiftikhar
yes:)

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