maths

let F(X) = X^99 + k
(a) When f(x) is diveded by x+1,the remainder is 1.Find the value of k.
(b) Hence, find the remainder when 9^99 is divided by 10.

(a)
R
=F(-1)
=(-1)^99+k
=-1+k
but R=1
so -1+k=1
k=2
(b)
F(9)
=9^99 + 2
F(9)+8=9^99 + 10
since when F(9) is diveded by 10,the remainder is 1 by part (a) result
when 8 is diveded by 10,the remainder is 8
so when F(9)+8=9^99 + 10 is diveded by 10,the remainder
=1+8
=9