lecture 1.4 to 1.5 bt
TRANSCRIPT
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)