maths-remainder

2011-11-24 6:36 am

a) find the remainder when (x^999)-3x is divided by x-1 and x+1 respectively
b) find the remainder when 7^999 is divided by 6
c) find the remainder when 7^999 is dividedby 8

更新1:

ans of b is 1 ans of c is 7

回答 (2)

用戶28092

2011-11-24 9:59 am

✔ 最佳答案

a.
f(x) = (x^999) - 3x
f(1) = 1 - 3(1) = -2
f(-1) = (-1)^999 - 3(-1) = 2

b.
put x = 7, f(7) = 7^999 - 3(7) when divided by 6, let Q be the quotient and the remainder = -2 as from (a)
7^999 = Q x 6 - 2 + 21 => (Q+3) x 6 + 1, the remainder = 1

c.
put x = 7, f(7) = 7^999 - 3(7) when divided by 8, let Q be the quotient and the remainder = 2 as from (a)
7^999 = Q x 8 + 2 + 21 => (Q+2) x 8 + 7, the remainder = 7
remarks: we always show positive remainder when it divided by a real number, not a function

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匿名

2011-11-25 1:37 am

Sorry"我睇漏左個-3x ;P

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