Intermediate Algebra (11th edition)

1.Apolynomialis an algebraic
expression made up of
A.a term or a finite product of
terms with positive coefficients
and exponents
B.the sum of two or more terms
with whole number coefficients
and exponents
C.the product of two or more terms
D.a term or a finite sum of terms
with real number coefficients and
whole number exponents.

2.Amonomialis a polynomial with

A.only one term

B.exactly two terms

C.exactly three terms

D.more than three terms.

3.Abinomialis a polynomial with

A.only one term

B.exactly two terms

C.exactly three terms

D.more than three terms.

4.Atrinomialis a polynomial with

A.only one term

B.exactly two terms

C.exactly three terms

D.more than three terms.

5.TheFOILmethod is used for

A.adding two binomials

B.adding two trinomials

C.multiplying two binomials

D.multiplying two trinomials.

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

ANSWERS
1.D;Example: 2.A;Examples: 3.B;Example: 4.C;Example:
5.C;Example:
FOI L

1 m+ 421 m- 32 =m 1 m 2 - 3 m+ 4 m+ 41 - 32 =m^2 +m- 12

5 x^3 + 2 x^2 - 7 - 4, 2x^3 , 15a^2 b 3 t^3 + 5 t 2 a^2 - 3 ab+b^2

5.1 Integer Exponents and Scientific Notation

Definitions and Rules for Exponents
For all integers mandnand all real numbers aandb,

Product Rule

Quotient Rule

Zero Exponent

Negative Exponent

Power Rules (a) (b)

(c)

Special Rules for Negative Exponents

Scientific Notation
A number is in scientific notation when it is expressed
in the form

a: 10 n, where and 1 ◊|a|< 10 nis an integer.

a 1 a,bZ 02

a

b

b

n

a

b

a

b

n
ana 1 aZ 02

1

a

b

n

1 a,bZ 02

an

bm



bm

an

1 aZ 02

1

an

an

a 1 bZ 02

a

b

b

n



an

bn

1 am 2 namn 1 ab 2 mambm

a-n 1 aZ 02

1

an

a^0  1 1 aZ 02

1 aZ 02

am

an

amn

am#anamn

Apply the rules for exponents.

,

,

,

Write 23,500,000,000 in scientific notation.

Write in standard notation.

4.3* 10 -^6 =0.0000043

4.3* 10 -^6

23,500,000,000=2.35* 1010

a

4

7

b

• 2
  = a

7

4

b

2

4 -^3 =a

1

4

b

3

5 -^3

4 -^6

=

46

53

1

3 -^2

= 32

a

2

3

b

5

=

25

35

16324 = 612 15 p 24 = 54 p^4

5 -^2 =

1

52

270 =1, 1 - 520 = 1

25

23

= 22

34 # 32 = 36

QUICK REVIEW

CONCEPTS EXAMPLES

7.2 Adding and Subtracting Rational Expressions

Add or subtract polynomials by combining like terms.

=- 2 x^4 + 2 x^2 +x

15 x^4 + 3 x^22 - 17 x^4 +x^2 - x 2

(continued)

CHAPTER 5 Summary 309