Question#1. The polynomial of degree 4, P ( x ) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = 2 . It goes through the point ( 5 , 21 ) . Find a formula for P (x).

Question#2. Expand the expression using the Binomial Theorem: (4x - 2)^5=

Question#3. The count in a bacteria culture was 200 after 20 minutes and 1800 after 30 minutes. Assuming the count grows exponentially, 1. What was the initial size of the culture? 2. Find the doubling period 3. Find the population after 85 minutes 4. When will the population reach 15000