The remainders when a polynomial P(x) is divided by x-2 and x+1 are respectively 3 and -2. The remainder when P(x) is divided by (x^2-x-2)is K(x). What is the value of K(-4) ?

- Loser66

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- Loser66

@zzr0ck3r Please.

- Loser66

@dan815 @ikram002p

- anonymous

yes please

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## More answers

- ikram002p

for tomorrow xD

- Loser66

It's ok, friend. It is not my problem, it is from other asker, I just help him to post it here because I don't know how to solve. :(

- ikram002p

Hint:-
(x-2) (x+1)=x^2-x-2
so
The remainder when P(x) is divided by (x^2-x-2)is K(x) ={The remainders when P(x) is divided by x-2) *{The remainders when P(x) is divided by x+1)
k(X)=3*-2

- Loser66

hey, go to bed, my friend. It is not that. K(x) =ax +b, it is a first degree polynomial.

- ikram002p

i should do that lol

- Loser66

hehehe.. I am using group theory to solve it or remainder theorem, but it sounds awkward hehehe... not know how to solve it yet.

- Loser66

\(P(x) = a_nx^n+a_{n-1}x^{n-1}+...............+a_0\)
what??? I saw @electrokid really???

- anonymous

yo

- Loser66

hey, is it you?? @electrokid or the net is crazy??

- Loser66

wwwwwwoaaaaaaah, how are you??
@Francesco1907 Sorry friend, I am so excited now, can't think anything.

- anonymous

ok still waiting for the answer

- anonymous

isnt this the remainder theorem?
If remainder of division by polynomial \(P(x)\) by \((x-a)\) is \(b\), then, \(P(a)=b\).

- Loser66

Yes, it is.

- Loser66

P(2) =3
P(-1) =-2
so??

- anonymous

P(x) = (x^2 - x- 2)Q(x) + K(x)
P(2) = K(2) =3
P(-1) = K(-1) = -2
K(x) = ax + b
So, 2x + b = 3
-1x + b = -2
solve these to get K(x)

- anonymous

so, we follow that \[P(2)=3\] and \[P(-1)=-2\]
\[P(x)=(x-2)(x+1)K(x)\]
so, \[K(x)=(3)(-2)\] i.e., indepemdemt of x

- Loser66

@electrokid I don't think so. \(P(x) = M(x) (x+2)(x-1) + K(x) \)

- Loser66

@adxpoi I think you are right.

- Loser66

but the equations are
2a+b =3
-a+b = -2

- anonymous

Yup, @adxpoi got it :)

- Loser66

@Francesco1907 take it, please. You have to do the rest.

- anonymous

Can I ask 1 more question

- anonymous

Please

- anonymous

Yeah sorry my bad, replace x by a in my last post :P

- Loser66

@Francesco1907 post a new one by yourself.

- anonymous

##### 1 Attachment

- Loser66

hey, it is 0, I think and it is not hard to see it, right? just take derivative and plug pi/10 in.

- anonymous

nope we found it its -5 mate

- Loser66

how? show me. Don't forget chain rule

- anonymous

solve me 57 while I am solving your question

##### 1 Attachment

- Loser66

I got -1/5

- anonymous

thats not the correct answer mate

- amilapsn

For the earlier question K(4) can be found using this method too.. (Using similar method you can find K(-4))
|dw:1440136503090:dw|

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