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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
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

This Question is Closed

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1obviously Q(1) = 4 and Q(1) = 8 by the remainder theorem

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2find the two values of x

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2x^21=(x1)(x+1) so x=1 and x=1 put one by one in equation

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2so the reminder is 32

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I dont follow that...

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2as given in data reminder for (x1)=4 and for (x+1)=8 so for x^21=(x1)(x+1)=4*8=32

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I don't think that's correct.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I'd dont think this is particularly different  I'm just missing something

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2O.o so what you think huh ? It is correct bro

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2so you just confused get calm and think on it for a minute

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I dont' know  but I don't think your logic is correct

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I'm going to look up the answer . I am confused  you are right there!! lol

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2yea! go an look the answer perhaps then you will believe on my answer

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2no way it can't be

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2take a screen short

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I'm helping my grandson with his maths revision. Well that's the answer in the book.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I haven't got a scanner

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2it's very simple .. ok tell me how they get 4 when they divide equation by (x1) huh ?

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2ok ganesh is here he can justify better now

welshfella
 one year ago
Best ResponseYou've already chosen the best response.14 is the remainder and = q(1)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4Firstly, notice that we get a polynomial as remainder that is one degree less than whatever we're dividing by

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4for example, (x^5+2x+1)/(x^21) gives a remainder that looks like \(ax+b\) yes ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4similarly (x^100 + x+1)/(x^10 + 1) gives a remainder that looks like \(ax^9+bx^8+\cdots\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4the degree of remainder is always one less than the degree of bottom

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1so the remainder in this case must be of the form ax + b?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4right, so lets suppose \[Q(x) = F(x)*(x^21)+\color{red}{ax+b}\] our goal is to find that red part

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4since we know that \(Q(1)=4\) and \(Q(1)=8\), plug them in and get two equations

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2ganesh what you said about the given that reminder of that equation is 4 when divided by (x1) where is x term with 4 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4\[Q(1) = F(1)*(1^21)+\color{red}{a*1+b} \implies 4 = \color{red}{a+b} \tag{1}\] \[Q(1) = F(1)*((1)^21)+\color{red}{a(1)+b} \implies 8 = \color{red}{a+b} \tag{2}\] two equations and two unknowns, we can solve them

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4for that, we may think that the coefficient of x is 0 @sohailiftikhar

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1thats really clever Thanx ganesh

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4np, im getting the remainder is \(2x+6\) looks the options are wrong

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1yes i got that too b = 6 ans a = 2

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1I'll just recheck the answer in the book

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1Yes thats the answer in the book. Well mistakes are made

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4happens... our method is pretty robust and straightforward, nothing that could go wrong..

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.2from which grades book u got that problem bro ?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1Oh 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...

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1Open study is a great place to study . There is a wealth a talent here.
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