lecture 1.1 to 1.3 bt
TRANSCRIPT
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WELCOME BACK!
MAT153
College Math and Statistics
BRAD THOMPSON
Class Meets: M,W E318
8:30 – 10:20
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Today’s Agenda
• Syllabus
• Course Information
• Class Procedures
• Questions?
• Sections 1.1 – 1.3
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Simplifying / Evaluating Expressions
“P.E.M.D.A.S.”
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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
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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
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Inequality / Interval Notation
−5 < 𝑥 < 4
−5 < 𝑥 ≤ 4
𝑥 ≥ 3
𝑥 < 2
)4,5(
]4,5(
),3[
)2,(
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Absolute Value
0||
0||
,
xifxx
xifxx
xnumberrealanyfor
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Absolute Value
|6| |6|
|43| |2|
|48| |85|
6 6
7 2
4 13
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Properties of Exponents
yxx 23 25 yx
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Properties of Exponents
25xy 2225 yx
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Properties of Exponents
23 )6( yx 2636 yx
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Properties of Exponents
05 0x
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Anatomy of a Polynomial
coefficients
423 2 xx
Degree = highest exponent
constant
term
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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
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Adding and Subtracting Polynomials
−2p3 − 5p + 7 + −4p2 + 8p + 2
3y3 + 9y2 − 11y + 8 − −4y2 + 10y − 6
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Multiplying Polynomials
Use the Properties of exponents
and the Distributive Property
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Multiplying Polynomials
Find each of the given products.
2a 4a2 − 6a + 8
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Multiplying Polynomials
Find each of the given products.
2k + 3 4k3 − 3k2 + k
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Multiplying Polynomials
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Multiplying Polynomials
Multiply.
8r + 3 r − 1
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Greatest Common Factor
Find the GCF of
12, 27, & 36
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Greatest Common Factor
Find the GCF of
15𝑥3, 12𝑥, & 9𝑥2
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Factoring
Can think of factoring as
the opposite of
distributing(multiplying).
This means that we’re
actually dividing.
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Factoring
“What is common to
all terms that we can
take out?”
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Greatest Common Factor
Factor out the greatest common factor.
5𝑦 − 15𝑥𝑦 3𝑥 + 7 5 − 4 3𝑥 + 7 3
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Greatest Common Factor
Factor out the greatest common factor.
5𝑥3 + 55𝑥2 + 10𝑥 3 𝑥 + 6 2 + 6 𝑥 + 6 4
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Factoring Quadratics
Polynomials of degree 2
mm
x
xx
43
9
946
2
2
2
?
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Factoring Quadratics
This can be thought of as the
reverse of “F.O.I.L.”
And you can always check
your answer!
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Factoring Quadratics
𝑦2 + 8𝑦 + 12
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Factoring Quadratics
𝑥2 + 4𝑥 − 5
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Factoring Quadratics
15𝑢2 + 4𝑢 − 4
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Factoring Quadratics
12𝑦2 + 7𝑦 − 10
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Factoring Quadratics
35 2 xx
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Factoring Polynomials
Special CasesDifference of Squares (p. 24)
𝑥2−𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦
𝑥2 − 25
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Factoring Polynomials
Special CasesDifference of Squares
𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦
9𝑝2 − 16
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Factoring Polynomials
Special CasesDifference of Squares
𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦
49𝑎2 + 9
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Chapter 1 Exam
• Monday 1/26
–Covers 1.1 – 1.7
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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)