Expand the polynomial f(n)=(n-0)(n-1)(n-2)(n-3)(n-4)

[Mellie]

(A)
Expand the polynomial f(n)=(n-0)(n-1)(n-2)(n-3)(n-4).

(Write the terms of your polynomial in order of decreasing degree, such as [tex]n^9+n^7+3[/tex].)

(B)
For the numbers n=0 through n=4 compute the remainder when [tex]n^5-n[/tex] is divided by 5. What is the sum of these five remainders?

(C)
For a certain positive integer [tex]n, n^2[/tex] gives a remainder of 4 when divided by 5, and [tex]n^3[/tex] gives a remainder of 2 when divided by 5. What remainder does n give when divided by 5?

[Guest]

A)n^5-10n^4+35n^3-50n^2+24n
B)0
C)3