1.
Factor completely and simplify: 
.
2.
What assumptions (list all of them) did you make in canceling/simplifying problem 1?
3.
Sketch the original function R(x) from problem 1, showing all salient features.
4.
Sketch the simplified expression from problem 1, treating it as a function of x. What salient features does this graph lack compared to #3?
5.
R(x) in problem 1 is an example of a _____________ function.
6.
Use synthetic division to prove that (x – ¾) is a factor of the polynomial 
.
7.
Write W(x) in problem 6 as a product of a linear polynomial and a cubic polynomial.
8.
Use long division to compute 
.
9.
Use algebra to verify your answer to #8 (i.e., check by multiplying).
10.
Use a messy value for x (write it here: x=_____________) to verify your answer to #8. The numerator (dividend) equals ________________ .
11.
Explain why your answer to #8 proves that for large values of x (as well as large negative values of x approaching –¥ ), the quotient is asymptotic to a line with slope –4 and y-intercept 3.
12.
Do #52 on p.363. The common denominator is ____________ .
13.
Do #61 on p.364. The common denominator is ____________ .
14.
Write the common denominator (do not solve) for problems 3-12 on p.368. Some have already been done for you.
3. Answer: 12
4. ____________
5. ____________
6. Answer: x – 1
7. ____________
8. ____________
9. Answer: (x + 1) (x – 1)
10. ____________
11. ____________
12. ____________
15.
What theorem guarantees that the only possible rational zeros of
2x3 – 15x2 + 2x – 3 are ± 1, ± ½, ± 3/2, and ± 3? ________________________