Ch. 5 Review
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Simplify the expressions.
1.
49𝑎3 𝑏−4 𝑐 7
35𝑎5 𝑏−2 𝑐 −9
2. (2𝑚5 𝑛−4 )(3𝑚−7 𝑛8 )
What is the end behavior of the function
3. f(x) = 𝑥 7 + 𝑥 5 − 𝑥 3 ?
Perform the indicated operation
4.
2𝑥 3 + 5𝑥 2 − 7𝑥 + 4 − (𝑥 3 − 3𝑥 2 − 4𝑥)
5. (2𝑥 3 − 11𝑥 2 + 13𝑥 − 44) ÷ (𝑥 − 5)
Factor the polynomial completely
6. 8𝑥 − 27
3
7. 𝑥 4 − 7𝑥 2 − 18
8. Find all the real zeros of
𝑓 𝑥 = 𝑥 3 + 𝑥 2 − 22𝑥 − 40
**Remember, real zeros are the same as
x-intercepts.
9. List all x-intercepts, local
maximums, and local minimums of
4
2
𝑓 𝑥 = 𝑥 − 9𝑥 + 4𝑥 + 12
10. Given the zeros −2𝑖 & 2 + 5 write
a polynomial equation in factored
form.
11. Factor the expression by grouping.
𝑥 3 + 3𝑥 2 − 4𝑥 − 12
12. Use long division to solve
6𝑥 4 + 7𝑥 2 + 4𝑥 − 17 ÷ (2𝑥 2 + 2𝑥 + 3)
13. Use synthetic division to find the
solutions of 𝑥 3 − 6𝑥 2 + 5𝑥 + 12 given
that 𝑥 − 3 is a factor.
14. Use 𝑓 𝑥 = 𝑥(𝑥 − 3)2 to answer the
following questions.

State the degree, type, and leading
coefficient of the polynomial function.
 Degree:
 Type:
 Leading
Coefficient:
14. Use 𝑓 𝑥 = 𝑥(𝑥 − 3)2 to answer the
following questions.
 What
is the max number of turns and max
number of x-intercepts the graph can have?

Turns:

X-intercepts:
14. Use 𝑓 𝑥 = 𝑥(𝑥 − 3)2 to answer the
following questions.
 Make
a table of values for the polynomial
function that contains at least 5 values.
X
Y
14. Use 𝑓 𝑥 = 𝑥(𝑥 − 3)2 to answer the
following questions.
 What
will the end behavior of the graph be?
14. Use 𝑓 𝑥 = 𝑥(𝑥 − 3)2 to answer the
following questions.
 Graph
the function.
14. Use 𝑓 𝑥 = 𝑥(𝑥 − 3)2 to answer the
following questions.
 State
the domain and range.
ANSWER KEY
7𝑐 16
 2 2
5𝑎 𝑏
6𝑛4
 2
𝑚
 f(x)
-> -∞ as x -> -∞ and f(x) -> +∞ as x -> +∞
 𝑥3
+ 8𝑥 2 − 3𝑥 + 4
 2𝑥
2
 (2𝑥
−𝑥
4
+8−
𝑥−5
2
− 3)(4𝑥 + 6𝑥 + 9)
ANSWER KEY
 (𝑥 2 +2)(𝑥
+ 3)(𝑥 − 3)
 X = -4, -2, 4
 x-intercepts: -3, -1, 2
local maximums: (-2, -16.7) and (2, 0)
local minimums: (0, 12.4)
 (𝑥
− 2𝑖)(𝑥 + 2𝑖)(𝑥 − 2 + 5 )(𝑥 − 2 − 5 )
 (x + 3)(x + 2)(x – 2)
 3𝑥
2
− 3𝑥 + 2 +
9𝑥−23
2𝑥 2 +2𝑥+3
ANSWER KEY
X
= -1, 3, 4
𝑓
𝑥 = 𝑥 3 − 6𝑥 2 +9x
 3,
2
cubic, 1
turns; 3 x-intercepts
 Table
 f(x)
-> -∞ as x -> -∞ and f(x) -> +∞ as x -> +∞
 Graph
 D:
all real numbers; R: all real numbers