Show that for every integer n, f (n) = (2 n3 + 3 n – 10 n + 5 n) is divisible by 7. %3D (Hint: use the Fermat's Theorem).

true of false:   (v) Given an integer n ≥ 2, [a]n ×n [0]n = [a]n for any integer a.

3. What is the coefficient of x³y²z² in the expansion of (x + y + 2z)⁹?

Note: The integer functions P(m,n) and C(m,n) are available for use. Use the binomial theorem to expand the following expressions. a. (1+x)7 b. (x+w)6 c. (x-w) 6 If you don't get this in 2 tries, you can get a hint.