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1. WELCOME BACK!
MAT153
College Math and Statistics
BRAD THOMPSON
Class Meets: M,W E318
8:30 – 10:20

2. Today’s Agenda
• Syllabus
• Course Information
• Class Procedures
• Questions?
• Sections 1.1 – 1.3

3. MyLabsPlus Homework
www.dtcc.mylabsplus.com
Login is same as DTCC.

4. Simplifying / Evaluating Expressions
“P.E.M.D.A.S.”

5. Evaluate each expression
1. 4 − 5 ∙ 6 + 6 2. 8 − −4 2 − −12
3.
2 3−7 +4 8
4 −3 + −3 −2
4.
62−3 25
62+13

6. Evaluating Variable Expressions
*Note: Use parentheses when substituting
1) −𝑥2
− 2𝑥 + 3
2) 𝑥2
− 2𝑥 + 3
3) −𝑥2
− 2𝑥 + 3
4) 𝑥2
− 2𝑥 + 3
3xlet 3xlet

7. Inequality / Interval Notation
−5 < 𝑥 < 4
−5 < 𝑥 ≤ 4
𝑥 ≥ 3
𝑥 < 2
)4,5(
]4,5(
),3[ 
)2,(

8. Absolute Value
0||
0||
,


xifxx
xifxx
xnumberrealanyfor

9. Absolute Value
 |6|  |6|
 |43|  |2|
 |48|  |85|
6 6
7 2
4 13

10. Properties of Exponents

 yxx 23 25
yx

11. Properties of Exponents
 2
5xy 22
25 yx

12. Properties of Exponents
23
)6( yx 26
36 yx

13. Properties of Exponents
0
5 0
x

14. Anatomy of a Polynomial
coefficients
423 2
 xx
Degree = highest exponent
constant
term

15. Polynomials
Polynomial Degree
Leading
Coefficient
Constant
Term
𝟒𝒙 𝟓 − 𝟐𝒙 𝟑 + 𝟑𝒙 − 𝟗
−𝟓𝒙 𝟒 + 𝟑𝒙 𝟐 +
𝟏
𝟑
𝒙 𝟐
− 𝟐𝒙 𝟑
+ 𝟒𝒙
−𝟏𝟕
5 4 -9
4 -5 1/3
3 -2 0
0 -17 -17

16. Adding and Subtracting Polynomials
−2p3
− 5p + 7 + −4p2
+ 8p + 2
3y3
+ 9y2
− 11y + 8 − −4y2
+ 10y − 6

17. Multiplying Polynomials
Use the Properties of exponents
and the Distributive Property

18. Multiplying Polynomials
Find each of the given products.
2a 4a2
− 6a + 8

19. Multiplying Polynomials
Find each of the given products.
2k + 3 4k3
− 3k2
+ k

20. Multiplying Polynomials

21. Multiplying Polynomials
Multiply.
8r + 3 r − 1

22. Greatest Common Factor
Find the GCF of
12, 27, & 36

23. Greatest Common Factor
Find the GCF of
15𝑥3
, 12𝑥, & 9𝑥2

24. Factoring
Can think of factoring as
the opposite of
distributing(multiplying).
This means that we’re
actually dividing.

25. Factoring
“What is common to
all terms that we can
take out?”

26. Greatest Common Factor
Factor out the greatest common factor.
5𝑦 − 15𝑥𝑦 3𝑥 + 7 5
− 4 3𝑥 + 7 3

27. Greatest Common Factor
Factor out the greatest common factor.
5𝑥3 + 55𝑥2 + 10𝑥 3 𝑥 + 6 2 + 6 𝑥 + 6 4

28. Factoring Quadratics
Polynomials of degree 2
mm
x
xx
43
9
946
2
2
2



?

29. Factoring Quadratics
This can be thought of as the
reverse of “F.O.I.L.”
And you can always check
your answer!

30. Factoring Quadratics
𝑦2
+ 8𝑦 + 12

31. Factoring Quadratics
𝑥2
+ 4𝑥 − 5

32. Factoring Quadratics
15𝑢2
+ 4𝑢 − 4

33. Factoring Quadratics
12𝑦2
+ 7𝑦 − 10

34. Factoring Quadratics
35 2
 xx

35. Factoring Polynomials
Special Cases
Difference of Squares (p. 24)
𝑥2−𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦
𝑥2
− 25

36. Factoring Polynomials
Special Cases
Difference of Squares
𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦
9𝑝2
− 16

37. Factoring Polynomials
Special Cases
Difference of Squares
𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦
49𝑎2
+ 9

38. Chapter 1 Exam
• Monday 1/26
–Covers 1.1 – 1.7

39. 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)