Math 1540 Test 1
3points each
Name:
1.) Use the given polynomial to answer the following questions.
7
6
5
4
3
2
( )
3
6
14
3
33
72
108
window: [5, 5, 1] and [150, 150,30]
P x
x
x
x
x
x
x
x
=
+




+
+
(a) Find all local and absolute extreme points and label each point. Round your answers to the
nearest hundredth.
Local minima: (2.02, 112.09), (2, 0)
Local maxima: (3, 0), (0.69, 137.27)
(b) Find the
rational
zero(s).
Hint:
all the factors of 108 are between 110.
List all the integers p that are factors of the constant term, 108
p:
±
1,
±
2,
±
3,
±
4,
±
6,
±
9,
±
12,
±
18,
±
27,
±
54,
±
108
List all the integers q that are factors of the leading coefficient, 1
q:
±
1
Form all possible ratios
p
q
.
p
q
:
±
1,
±
2,
±
3,
±
4,
±
6,
±
9,
±
12,
±
18,
±
27,
±
54,
±
108
Check 2:
1
3
6
14
3
33
72
108
2
2
10
8
12
30
126
108
1
5
4
6
15
63
54
0












Since P(2) = 0 then x – 2 is a factor.
Then
6
5
4
3
2
( )
(
2)(
5
4
6
15
63
54)
P x
x
x
x
x
x
x
x
=

+
+



