lecture 1.1 to 1.3 bt
TRANSCRIPT
WELCOME BACK!
MAT153
College Math and Statistics
BRAD THOMPSON
Class Meets: M,W E318
8:30 – 10:20
Today’s Agenda
• Syllabus
• Course Information
• Class Procedures
• Questions?
• Sections 1.1 – 1.3
Simplifying / Evaluating Expressions
“P.E.M.D.A.S.”
Evaluate each expression
1. 4 − 5 ∙ 6 + 6 2. 8 − −4 2 − −12
3. 2 3−7 +4 8
4 −3 + −3 −24.
62−3 25
62+13
Evaluating Variable Expressions
*Note: Use parentheses when substituting
1) −𝑥2 − 2𝑥 + 3
2) 𝑥2 − 2𝑥 + 3
3) −𝑥2 − 2𝑥 + 3
4) 𝑥2 − 2𝑥 + 3
3xlet 3xlet
Inequality / Interval Notation
−5 < 𝑥 < 4
−5 < 𝑥 ≤ 4
𝑥 ≥ 3
𝑥 < 2
)4,5(
]4,5(
),3[
)2,(
Absolute Value
0||
0||
,
xifxx
xifxx
xnumberrealanyfor
Absolute Value
|6| |6|
|43| |2|
|48| |85|
6 6
7 2
4 13
Properties of Exponents
yxx 23 25 yx
Properties of Exponents
25xy 2225 yx
Properties of Exponents
23 )6( yx 2636 yx
Properties of Exponents
05 0x
Anatomy of a Polynomial
coefficients
423 2 xx
Degree = highest exponent
constant
term
Polynomials
Polynomial DegreeLeading
Coefficient
Constant
Term
𝟒𝒙𝟓 − 𝟐𝒙𝟑 + 𝟑𝒙 − 𝟗
−𝟓𝒙𝟒 + 𝟑𝒙𝟐 +𝟏
𝟑
𝒙𝟐 − 𝟐𝒙𝟑 + 𝟒𝒙
−𝟏𝟕
5 4 -9
4 -5 1/3
3 -2 0
0 -17 -17
Adding and Subtracting Polynomials
−2p3 − 5p + 7 + −4p2 + 8p + 2
3y3 + 9y2 − 11y + 8 − −4y2 + 10y − 6
Multiplying Polynomials
Use the Properties of exponents
and the Distributive Property
Multiplying Polynomials
Find each of the given products.
2a 4a2 − 6a + 8
Multiplying Polynomials
Find each of the given products.
2k + 3 4k3 − 3k2 + k
Multiplying Polynomials
Multiplying Polynomials
Multiply.
8r + 3 r − 1
Greatest Common Factor
Find the GCF of
12, 27, & 36
Greatest Common Factor
Find the GCF of
15𝑥3, 12𝑥, & 9𝑥2
Factoring
Can think of factoring as
the opposite of
distributing(multiplying).
This means that we’re
actually dividing.
Factoring
“What is common to
all terms that we can
take out?”
Greatest Common Factor
Factor out the greatest common factor.
5𝑦 − 15𝑥𝑦 3𝑥 + 7 5 − 4 3𝑥 + 7 3
Greatest Common Factor
Factor out the greatest common factor.
5𝑥3 + 55𝑥2 + 10𝑥 3 𝑥 + 6 2 + 6 𝑥 + 6 4
Factoring Quadratics
Polynomials of degree 2
mm
x
xx
43
9
946
2
2
2
?
Factoring Quadratics
This can be thought of as the
reverse of “F.O.I.L.”
And you can always check
your answer!
Factoring Quadratics
𝑦2 + 8𝑦 + 12
Factoring Quadratics
𝑥2 + 4𝑥 − 5
Factoring Quadratics
15𝑢2 + 4𝑢 − 4
Factoring Quadratics
12𝑦2 + 7𝑦 − 10
Factoring Quadratics
35 2 xx
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
Chapter 1 Exam
• Monday 1/26
–Covers 1.1 – 1.7
Classwork / Homework
• Classwork
–Page 71: 15 – 47 odd
• Homework
– MyLabsPlus HW1
»Due Sunday 1/18, 11:59pm
• Read 1.4, 1.5
• Quiz Wednesday(extra credit)