Formulae and Polynomials

Let f(x) =x1997 +2.
a)Find the remainder when f(x) is divided by x-1.
f(1) = x1997 + 2 = 11997 + 2
= 3
the remainder when f(x) is divided by x-1 is 3
b)Hence find the remainder when 71997 +2 is divided by 6.
Let x = 7
So
6 = x – 1
f(x) = x1997 +2
f(1) = 11997 +2
= 3
the remainder is 3
c)Using the result obtained in (b), find the remainder when 71997 is divided by 6
so 71997 is divided by 6 is
3 – 2
= 1