More about Polynomials(1)

2012-02-19 7:38 am

30.(a)
When x^99+k is divided by x+1,the remainder is 1.Find the value of k.
(b)Hence,find the remainder when 9^99 divided by 10

更新1:

why 9^99=10xQ(x)-1 need change to 9^99=10{Q(x)-1)}+9 Sub x=9 into x^99=(x+1)Q(x)-1 ,whyQ(x) not sub x= 9 i.e Q(9)

回答 (1)

pingshek

2012-02-19 9:53 am

✔ 最佳答案

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2012-02-19 21:48:45 補充：
Why 9^99 = 10*Q(x)-1 need change to 9^99=10{Q(x)-1)}+9

Dividend = Divisor * Quotient + Remainder
From 9^99 = 10{Q(x)-1)} + 9 :
Dividend (被除數) = 9^99
Divisor (除數) = 10
Quotient (商數) = Q(x) - 1
Remainder = 9

2012-02-19 21:50:21 補充：
Sub x=9 into x^99=(x+1)Q(x)-1 ,whyQ(x) not sub x= 9 i.e Q(9)

Yes, Q(9) is better. However, the answer can be obtained by either using Q(x) or Q(9).

參考: miraco, miraco, miraco

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