Algebra 2
Chapter 5 Test Review #2
1. Factor the following expressions completely.
a. x 3  125
b. x 4  9 x 2  20
c. 27 x 3  8
d. 3 x 4  18 x 2  24
e. 16 x 4  1
f. x 4  27 x
2. Determine the value of k such that the given factor divides the polynomial expression
with a remainder of 4.
3x3  2 x 2  5 x  k
Factor: ( x  2)
3. Solve the following equations.
a. x 4  5 x 2  36  0
b. x 4  81  0
4. Use the graph of the following polynomial function to answer each question.
y
a) Determine the roots & their multiplicity.
___________________________
b) Write an equation of this graph in factored form.
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
_______________________________________
c) Identify the y-intercept. _____________
d) Describe the end behavior of the function.
5. Given the polynomial function f (x)  4 x 3  8x 2 15x  9 :
State the factors and find all the zeros of the function given that f (3)=0.
Write the function in factored form: ___________________
Identify the y-intercept: __________
Sketch the function on the provided axis.
6. Evaluate the following expression.
a.  x 4  8 x 2  3 x    x 2  2 x 
b.  x 3  8 x  33    x  2 
7. Write the equation in factored form of a polynomial function of least degree with a
a) leading coefficient of negative one whose graph passes through the x-axis at -6 and 1
and is tangent to the x-axis at 3. Sketch the graph.
b) leading coefficient of two whose graph changes concavity at -1, is tangent to the x-axis
at 2 and goes through the point (5, 0). Sketch the graph.
8. Write the equation in standard form of a polynomial function of least degree with a leading
coefficient of two whose graph is tangent to (-3,0) & goes through (4,0). Sketch the graph.
9.
Analyze and sketch the function below.


f ( x)  x 2  1 x 2  3x  4
a) Degree:
b) Leading Coefficient:
c) Zeros & multiplicity:
d) y-intercept:
e) End Behavior:

y
_____________________
_____________________
_____________________
-5
-4
-3
-2
-1
1
_____________________
_____________________
10. Describe the end behavior of the polynomial function.
a.)
f  x   3x 7  2 x 4  9
As x   , f  x   _____
As x  , f  x   _____
b.)
f  x    x  1  x  3 2 x  3
2
3
As x   , f  x   _____
As x  , f  x   _____
2
3
4
5
x
11. Use the graph below to answer the following questions.
a. On what interval is the function increasing?
b. What does  ,   represent?
c. What is the end behavior of the function?
d. What term best describes the point (-1, -3)?
e. What term best describes the point (2, 0)?
f. What terms described the point (0, 0)
g. Is f  4  or f 2 greater in value? Why?
12. Use your calculator to analyze the function. Sketch & label the graph.
Round to the thousandth place.
f ( x)  2 x 4  3x  4
Domain: _________________ Range: _________________
Increasing: __________________________________
Decreasing: _________________________________
y-intercept: ____________ Root(s): __________________
Extrema:
End Behavior:
How many imaginary zeroes does this function have? How do you know?