Question

The remainder of x³ divided by x²-x+1 is A, and the remainder of x^2007 by x²-x+1 is B. Find A and B

Answer 1

check the question once

Answer 2

the phrase : The remainder of x³ divided A by x²-x+1 is...
makes no sense

Answer 3

@rsadhvika, sorry. Was AFK and it was a mistype.

Answer 4

finding A is easy right

Answer 5

a is -1 b is -2007/x

Answer 6

Well, answer for B is -1. But A is right. Can you show the steps?

Answer 7

ya wait

Answer 8

did you get it

Answer 9

Yes, I did, thanks! Now I've got only to find B.

Answer 10

what's the question for b

Answer 11

Well, your answer states that B = -2007/x. But here it says the answer is also -1.

Answer 12

x^2007 by x²-x+1 is this the question

Answer 13

yes

Answer 14

i couldn't find once check the question

Answer 15

http://www.studyjapan.go.jp/en/toj/pdf/08-006.pdf Here is the question. It is the question number 2.

The answer is here: http://www.studyjapan.go.jp/en/toj/pdf/08-gakubu_answer.pdf. It is in page 5.

Answer 16

Well, I'm going to try. Wait a moment :)

Answer 17

oh its x to the power of 2007 i thought its 2007x2

Answer 18

Yea, haha.

Answer 19

as you got remainder -1 for x3 for every odd power you will get the same -1

Answer 20

And if it is even?

Answer 21

Is there a general rule?

Answer 22

no but i remember this type of problems
no one does division for such a long power they just use logic and shotcut's that's why they give a problem like x3 before it

Answer 23

K, I got it... Thanks.

Answer 24

anytime