more about polynomail exercise 7B (29,30)
29.(A) write down the highest possible degree of the remainder when a polynomail P(x) is divided by (x-1)(x+2).
(B)it is given that when P(x)in (a) is divided by x-1 and x+2,the remainders are -4 and -28 respectively.Find the remainders
when P(x) is divided by (x - 1)(x + 2).
30.(A)when x^99+k is divided by x+1,the remainders is 1. find the value of k.
(B)hence,find the remainder when 9^99 is divided by 10.
Thz a lots of your help!
PS:"they are the diamond question,i think they are very hard."
more about polynomail exercise
2010-09-09 6:13 am
回答 (2)
2010-09-09 6:42 am
✔ 最佳答案
29a) The highest degree is 129b)
P(x) = Q(x) (x-1)(x+2) + ax + b
P(1) = a+b = -4
P(-2) = -2a+b = -28
a = 8 b= - 12
So, when P(x) divided by (x-1)(x+2),
remainder = 8x-12
30a)
let P(x) : x^99 +k
P(-1) = (-1)^99 + k = 1
-1 + k = 1
k = 2
30b)
P(x) : x^99 +2
Put x = 9,
P(9) : 9^99 +2
It's given that if (9)^99 +2 is divided by (9)+1, the remainder is 1
It also means that when 9^99+2 is divided by10, the remainder is 1
So, we have when 9^99 divided by 10, remainder = 1+(1x10)-2 = 9
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