a). find the remainder when x^1000 + 6 is divided by x + 1 ...我計到7,唔知岩唔岩-_-..

b). i Using a). or otherwise, find the remainder when 8^1000 + 6 is divided by 9

ii.  What is the remainder when 8^1000 is divided by 9?

q(x) = quotient, r = remainder.

a)
f(x) = x^1000 + 6 = q(x)(x+1) + r
f(-1) = (-1)^1000 + 6 = q(x)(-1+1) + r
                           1 + 6 = r
-> r = 7

b)
for x = 8, x + 1 = 9
-> r = 7, by part(a)

c)
f(x) = x^1000 = q(x)(x+1) + r
f(-1) = (-1)^1000 = q(x)(-1+1) + r
-> r = 1