Show all work. How you get your answer is just as important, if not more important, than the answer itself. If you think it, write it!

- 6.
- (8 pts. each) For the polynomial function

use (synthetic or polynomial long) division to write f(x) as

(a) (x-2)g(x)+c

(b) (x+1)h(x)+d

- 1.
- (12 pts.) Show that the polynomial

has only one real root. (Hint: think positive vs. negative roots). What two consecutive integers does it lie between?

- 2.
- (12 pts.) Find all of the rational roots of the polynomial

- 3.
- (12 pts.) One root of the function

is 1+i (you DON'T need to check this!). Find all of the other roots.

- 4.
- (6 pts. each) Find the following numbers (write them in standard form):

(a): (1+Ö2i)(1-3i) =

(b): [(1+Ö2i)/(1-3i)] =

- 5.
- (15 pts.) Find all of the relevant asymptotes of the function

and use this information to help draw a graph of the function.

- 6.
- (10 pts.) Use the rules of logarithms to expand the following expression as much as possible:

- 7.
- (12 pts.) Solve for x:

- 8.
- (15 pts.) How long will it take your money to triple if it is invested at 12% interest, compounded 4 times per year? (You may leave your answer in terms of logs.)

File translated from T