I need help with question 2, 3 and 4 please. Thanks in advance.

Answer the following questions: 1. Prove that any polynomial of degree k is O (nk 2. By finding appropriate values ofc and no, prove that: f(n) 4 n log2 n + 4 n2 + 4 n iso(n2). 3. Find functions fi and fi such that both fi(n) and /i(n) are O(g(n)), but fi(n) is not OG(n)) 4. Determine whether the following statements are true or false. Briefly justify your answer. a. Iff(n) is (g(n)), then 2r0% (29(n)). b. f(n)g(n) is (min (f (n). g(n)) c. 2na is O(2"), where a is a constant