MAT 171 Chapter 4 Review Problems
1. State whether the following are polynomials or not. For those which are, give the degree, leading term
and leading coefficient. For those which aren’t state why.
(a) Px   3
(c)
2
(b) P x   5 x  x  2 x  7
P x   17 x 3  3x 
7
4
x2
(d) Px   7 x 8  146 x 5  x 2 
2
3
2. Given Px   3xx  4 2 x  3 2  x 
5
2
4
a) List the zeros and their multiplicities for Px  and state whether the graph touches or crosses the
axis at each intercept.
b) The end behavior of Px  resembles a function of the form y  ax n find the function.
c) Sketch Px 
3. Given Px   2 x 5  12 x 4  18 x 3
a) The end behavior of Px  resembles a function of the form y  ax n what is that function.
b) List the zeros and their multiplicities for Px  and state whether the graph touches or crosses the
axis at each intercept.
c) Sketch Px 
4. Given Rx  
2x  4x  1
x  1x  22
(a) Find any holes in the graph of Rx 
(c) Find any vertical asymptotes for Rx 
(e) Sketch Rx 
2 x 2  8x  8
5. Given Rx   2
x  3x  4
a) Find any holes in the graph of Rx 
b) Find any intercepts of Rx 
c) Find any vertical asymptotes for Rx 
d) Find any horizontal asymptotes for Rx 
e) Sketch Rx 
(b) Find any intercepts of Rx 
(d) Find any horizontal asymptotes for Rx 
6. Find the equation of Rx  shown on the graph below.
7. Solve xx  2  15 (give solution in interval notation)
x2
 2 (give solution in interval notation)
x3
For f x   3x 3  7 x 2  4
8. Solve
9.
a) What is the remainder when f x  is divided by x  1
b) Show that x  2 is a factor of f x 
c) Factor f x  completely
10. A polynomial Px  with real coefficients has zeros 3,2  4i,5  7 and 2 11 .
a) What other zeros must Px  have?
b) What is the minimum degree of Px  ?
11. Find the equation of Rx  shown on the graph below.
12. Find the equation of Rx  shown on the graph below.
13. Find the equation of Rx  shown on the graph below.
14. Find the equation of Rx  shown on the graph below.