Today’s Agenda

• Attendance / Announcements

– Chapter 1 Exam on Monday 1/26

• Questions from HW?

• Section 1.4 Rational Expressions

• Section 1.5 Exponents

MyLabsPlus HW

• www.dtcc.mylabsplus.com

BlackBoard Resources

www.my.dtcc.edu

Factoring Polynomials

Special CasesDifference of Squares (p. 24)

𝑥2−𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦

𝑥2 − 25

Factoring Polynomials

Special CasesDifference of Squares

𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦

9𝑝2 − 16

Factoring Polynomials

Special CasesDifference of Squares

𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦

49𝑎2 + 9

FactoringRemember to always factor out the

G.C.F. and keep factoring until you

can’t factor anymore!

xxx 963 23

1.4 Rational ExpressionsAn expression that can be written

as the quotient of two polynomials.

2

532 2

x

xx

1

8

x x

2

note*: We need to make sure…..

Simplifying Rational Expressions

Cancellation Property

Q

P

QS

PS

55

x

x

Simplifying Rational Expressions

Cancellation Property

44

x

x

Simplifying Rational Expressions

Cancellation Property

Simplify each expression…

9𝑚

27𝑚3

10𝑧+5

20𝑧+10

𝑟2−𝑟−6

𝑟2+𝑟−12

327

9

m

m

2

1

3

1

m

23

1

m

1210

125

z

z

2

1

34

23

rr

rr

4

2

r

r

Simplify each expression…

𝑧2 + 4𝑧 + 4

𝑧2 − 4

Multiplying

Rational Expressions (p. 29)

Same as fraction arithmetic

“Multiply straight across…top and

bottom”

Multiply

2𝑢2

8𝑢4∙10𝑢3

9𝑢

5

5

72

20

u

u

18

5

Dividing

Rational Expressions (p. 29)

Same as fraction arithmetic

“Dividing by a fraction

Multiply by the reciprocal”

Perform each operation…6𝑥2𝑦

2𝑥÷

21𝑥𝑦

𝑦

𝑛2 − 𝑛 − 6

𝑛2 − 2𝑛 − 8÷

𝑛2 − 9

𝑛2 + 7𝑛 + 12

Adding / Subtracting

Rational Expressions

“Just like with fractions…We need

a….”

Perform each operation…

4

3𝑧+

5

4𝑧

8

𝑦+2−

3

𝑦

Complex Fractions (p. 33)

1

3

2

x

x

Section 1.5 ExponentsMore Properties of Integer

Exponents

Simplify…

6

9

x

x

x

yx43

Exponents…continuedMore Properties of Integer

Exponents

Simplify…

5

𝑥𝑦

3 5𝑣23

2𝑣 4

Exponents…continuedNegative Exponents

We usually want our answers to be

written only in Positive

Exponents…So we need to rewrite.

Simplify…

10−1 35 xy

Exponents…continuedNegative Exponents

Simplify…2

2

y

x2

3

43

z

yx

Properties of Exponents

• You’ll need to know the entire

table of properties on page 41.

Rational Exponents Radicals

𝒂 𝟏 𝒏 is defined to be

the “nth root of a.”

You can think of fraction exponents

as radicals…and vice versa

Rational Exponents Radicals

x“Invisible Numbers!”

Rational Exponents (p. 44)

So, if n is an even integer and a ≥ 0;

or if n is odd, then

naan1

When dealing with radicals/roots, we

always need to think about…

Rational Exponents Radicals

And if the root exists…

nm

aan m

Rewrite in radical notation

32

x 31

5x

3 2x 3 5x

Rewrite in exponent notation

5x3 7 33 x

Properties of Radicals (p. 44)

Radicals can be separated across

multiplication and division.

Properties of Radicals

We use these properties when we

simplify roots.

72

Properties of Radicals

We use these properties to simplify

roots.

155

Properties of Radicals

80245205

Remember, we can only add “like”

terms

Properties of Radicals

2353

Classwork / Homework

• Classwork

–Page 71: 51 – 93 odd

• Homework

– MyLabsPlus HW1

»Due Sunday 1/18, 11:59pm

• Read 1.6, 1.7 (No Class Monday 1/19)

• Quiz Today (extra credit)