326
CHAPTER 5
Exponents, Polynomials, and Polynomial Functions
Solve.
101.
1
x
2
+
x

6
21
3
x
2

14
x

5
2
=
0
102.
1
x
2

9
21
x
2
+
8
x
+
16
2
=
0
With new plugin hybrid autos and electric autos, it is very difficult
to predict future sales of hybrids. One forecast is the equation
y
=
3
x
2

25
x
+
345
, where x is the number of years past 2007
and y is the number of hybrid sales in thousands. Use this equation
for Exercises 103 and 104.
103.
Let
y
=
317 and solve the resulting quadratic equation by
factoring.
104.
Write a sentence explaining the meaning of the larger so
lution of Exercise 103.
105. Explain how solving 21x321x12=0 differs from solving 2x1x321x12=0.
1.
A(n)
is a finite sum of terms in which all variables are raised to nonnegative integer powers and no vari
ables appear in any denominator.
2.
is the process of writing a polynomial as a product.
3.
are used to write repeated factors in a more compact form.
4.
The
is the sum of the exponents on the variables contained in the term.
5.
A(n)
is a polynomial with one term.
6.
If
a
is not 0,
a
0
=
.
7.
A(n)
is a polynomial with three terms.
8.
A polynomial equation of degree 2 is also called a(n)
.
9.
A positive number is written in
if it is written as the product of a number
a
, where 1
…
a
6
10, and a power
of 10.
10.
The
is the largest degree of all its terms.
11.
A(n)
is a polynomial with two terms.
12.
If
a
and
b
are real numbers and
a
#
b
=
,
then
a
=
0 or
b
=
0.
106.
Explain why the zero factor property works for more than two numbers whose product is 0.
107. Is the following step correct? Why or why not?
108. Are the following steps correct? Why or why not?
109.
5, 3
110.
6, 7
111.

1, 2
112.
4,

3
113.
Draw a function with intercepts
1

3, 0
2
,
1
5, 0
2
, and (0, 4).
114.
Draw a function with intercepts
1

7, 0
2
,
a

1
2
, 0
b
, (4, 0),
and
1
0,

1
2
.
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Chapter 5 Highlights
327
DEFINITIONS AND CONCEPTS
EXAMPLES
Section 5.1
Exponents and Scientific Notation
Product rule:
a
m
#
a
n
=
a
m
+
n
Zero exponent:
a
0
=
1,
a
0
Quotient rule:
a
m
a
n
=
a
m

n
,
a
0
Negative exponent:
a

n
=
1
a
n
,
a
0
A positive number is written in
scientific notation
if it is
written as the product of a number
a
, where 1
…
a
6
10,
and an integer power of 10:
a
*
10
r
.
x
2
#
x
3
=
x
5
7
0
=
1,
1

10
2
0
=
1
y
10
y
4
=
y
10

4
=
y
6
3

2
=
1
3
2
=
1
9
,
x

5
x

7
=
x

5

1

7
2
=
x
2
Numbers written in scientific notation
568,000
=
5.68
*
10
5
0.0002117
=
2.117
*
10

4
Section 5.2
More Work with Exponents and Scientific Notation
Power rules:
(
a
m
)
n
=
a
m
#
n
(
ab
)
m
=
a
m
b
m
a
a
b
b
n
=
a
n
b
n
,
b
0
(7
8
)
2
=
7
16
(2
y
)
3
=
2
3
y
3
=
8
y
3
a
5
x

3
x
2
b

2
=
5

2
x
6
x

4
=
5

2
#
x
6

1

4
2
=
x
10
5
2
,
or
x
10
25
Section 5.3
Polynomials and Polynomial Functions
A
polynomial
is a finite sum of terms in which all variables
have exponents raised to nonnegative integer powers and no
variables appear in a denominator.