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1. (8
pts) Form a polynomial of degree 5, with
a zero of multiplicity 1 at x = -3, a
zero of multiplicity 2 at x = 4, and
a zero of multiplicity 1 at x = 1 + 3i .
Please leave it in factored form.
2. 
(7
pts) Circle the polynomial functions in
the list which might have the given graph.
a. 
b. 
c. 
d. 
3. (7
pts) Find the domain of 
.
4. Solve
each of the following inequalities. The
answers should be strangely similar,
yet distinctly different.
a. (5
pts) 
b. (5
pts) 
5. (7
pts) Use the Remainder Theorem and synthetic division to evaluate 
for 
.
6. (7
pts) Use Descartes’ Rule of Signs to determine the possible number of
positive and negative real zeros of 
. You don’t need to
find any of the zeros.
7. (7
pts) Use the Rational Zeros Theorem to list all
the possible rational zeros of 
. You don’t need to
find which ones (if any) actually work.
Just list the possibilities.
8. (7
pts) Use the Intermediate Value Theorem to show that 
has a zero in the
interval 
.
9. Let
.
a. (5
pts) Find 
.
b. (5
pts) Find the domain of the composite
function 
.
10. (5
pts) Given that 
, find functions f and g
such that 
.
11. (10
pts) Find all complex zeros of 
.
12. (5
pts) Use the complex zeros from #10 to
write in factored form.
13. (10
pts) The graph of a one-to-one
function f is given. Draw the graph of the inverse function 
. For convenience (and
as a hint), the graph of 
is given. (This one is fairly tricky).
Bonus Page.
(5
pts) Find a bound on the real zeros
of 
.
(5 pts) Let 
. Find 
.