5.1, 5.2, 5.3 properites of exponentsvvcforme.com/math-videos/a/lecture_guide 42_ch5-6.pdfbinomial...

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48 48 5.1, 5.2, 5.3 – Properites of Exponents last revised 6/7/2014 Properites of Exponents 1. βˆ™ = + 2. = βˆ’ 3. ( ) = βˆ™ 4. 0 =1 5. βˆ’ = 1 *Simplify each of the following: a. 4 βˆ™ 8 = b. 5 βˆ™ 7 βˆ™= c. 5 6 βˆ™5 11 = d. 14 9 = e. 6 11 14 3 7 12 = f. (2 2 15,000 ) 0 = g. 3 0 = h. (3) 0 = i. βˆ’4 2 = j. 3 βˆ’4 βˆ’2 8 = Negative exponents are NOT considered to be simplified. Do NOT leave them in final answers!

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Page 1: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

48

48

5.1, 5.2, 5.3 – Properites of Exponents last revised 6/7/2014

Properites of Exponents

1. π‘₯π‘Ž βˆ™ π‘₯𝑏 = π‘₯π‘Ž+𝑏

2. π‘₯π‘Ž

π‘₯𝑏 = π‘₯π‘Žβˆ’π‘

3. (π‘₯π‘Ž)𝑏 = π‘₯π‘Žβˆ™π‘

4. π‘₯0 = 1

5. π‘₯βˆ’π‘Ž =1

π‘₯π‘Ž

*Simplify each of the following:

a. π‘₯4 βˆ™ π‘₯8 =

b. π‘₯5 βˆ™ π‘₯7 βˆ™ π‘₯ =

c. 56 βˆ™ 511 =

d. π‘₯14

π‘₯9 =

e. π‘₯6𝑦11𝑧14

π‘₯3𝑦7𝑧12=

f. (2π‘₯2𝑦15,000)0 =

g. 3π‘₯0 =

h. (3π‘₯)0 =

i. π‘₯βˆ’4

π‘₯2=

j. π‘₯3π‘¦βˆ’4

π‘₯βˆ’2𝑦8=

Negative exponents are NOT considered to be

simplified. Do NOT leave them in final answers!

Page 2: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

49

49

k. (3

5)

2=

l. (3π‘₯2𝑦3)4 =

m. (2π‘₯2𝑦3)2(βˆ’3π‘₯𝑦4)2 =

n. π‘₯βˆ’4

π‘₯βˆ’8=

o. 5βˆ’1

5=

p. 6βˆ’2 =

q. βˆ’6βˆ’2 =

r. βˆ’12π‘₯βˆ’4π‘¦βˆ’3

48π‘₯βˆ’7𝑦5 =

s. (3π‘₯βˆ’2𝑦4

6π‘₯5π‘¦βˆ’7)βˆ’3

=

6. Simplify: (βˆ’3π‘’βˆ’3

π‘€βˆ’6 ) (βˆ’2𝑒2𝑣3𝑀2)βˆ’3

Simplify each:

5π‘₯βˆ’3 73 βˆ™ 711 5(π‘₯2𝑦3)0

Page 3: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

50

50

5.4 – Scientific Notation

Scientific notationis a shorthand notation for

writing extremely small or large numbers.

Notation:

*Write each using scientific notation:

1. 9,374,000

2. 19.4 trillion

3. 0.000381

*Write each in standard form:

4. 4.71 x 108

5. 3.21 x 10βˆ’5

*Multiply. Write your answers in scientific notation:

6. (3.5 x 1011) (4.0 x 1023

)

7. (2.45 x 1017) (3.5 x 1012

)

*Divide. Write your answers in scientific notation:

8. 12.5 x 10βˆ’4

2.5 x 1019

9. 2.4 x 108

4.8 x 1042

Page 4: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

51

51

5.5 – Adding and Subtracting Polynomials

monomial

binomial

trinomial

polynomial

Vocabulary: π‘Žπ‘₯𝑛 + 𝑏π‘₯π‘›βˆ’1 + β‹― + 𝑐π‘₯ + 𝑑

*Given: 5π‘₯7 + 4π‘₯6 + 3π‘₯5 β‹― + 5π‘₯ βˆ’ 11, find

the following:

a. leading coefficient

b. constant term

c. degree of the second term

d. degree of the polynomial

If a term has more than one variable, its degree

is the ________ of its exponents.

*What is the degree of the expression 5π‘₯2𝑦7?

*Add: (3π‘₯2 + 5π‘₯ βˆ’ 2) + (7π‘₯2 βˆ’ 9π‘₯ + 13)

*Add:

5π‘₯3+3π‘₯2 +118π‘₯3βˆ’9π‘₯2+5π‘₯βˆ’3

*Find the perimeter:

*Subtract: (3π‘₯2 + 5π‘₯ + 11) βˆ’ (π‘₯2 + 7π‘₯ βˆ’ 4)

*Subtract:

5π‘₯3βˆ’2π‘₯2+4π‘₯βˆ’92π‘₯3+7π‘₯2βˆ’11π‘₯+8

6x - 4

6x - 4

5x+3

8x+2

8x+2

Page 5: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

52

52

5.6 – Multiplying Polynomials

*Multiply each of the following:

1. (βˆ’3π‘₯4)(5π‘₯5)

2. 4π‘₯(3π‘₯ βˆ’ 7)

3. 5π‘Ž2𝑏3𝑐4(3π‘Žπ‘7 βˆ’ 5π‘Žπ‘2𝑑5)

4. (π‘₯ + 5)(π‘₯ βˆ’ 3)

5. (2π‘₯ βˆ’ 3)(3π‘₯ + 5)

6. (3π‘₯ βˆ’ 5)(2π‘₯ + 4)

7. (5π‘₯ βˆ’ 1)(π‘₯ + 8)

8. (4π‘₯ βˆ’ 7)(4π‘₯ + 7)

9. (π‘Ž + 𝑏)(𝑐 + 𝑑)

10. (3π‘₯ βˆ’ 2)(π‘₯2 + 4π‘₯ βˆ’ 7)

11. (5π‘₯ + 7)(3π‘₯ βˆ’ 2)

12. (3π‘₯ βˆ’ 2)2

13. (3π‘₯2𝑦4)2

Page 6: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

53

53

Mini-Review of Sections 5.1 – 5.6

1. Simplify: βˆ’5π‘₯βˆ’3𝑦

10π‘₯4π‘¦βˆ’5

2. Multiply: (4.3 x 108) (3.0 x 1017

)

3. Divide: 0.6 x 10βˆ’15

2.4 x 1011

4. Multiply: βˆ’5π‘₯2𝑦3𝑧(8π‘₯𝑦𝑧5 βˆ’ 4π‘₯𝑦2𝑧3)

5. Multiply: (3π‘₯2 + 4)(2π‘₯2 βˆ’ 7)

6. Multiply: (π‘₯ βˆ’ 3)(π‘₯2 + 3π‘₯ + 9)

7. Multiply: (π‘₯2 + 4π‘₯ βˆ’ 2)(π‘₯2 + π‘₯ βˆ’ 5)

8. Calculate the area of the larger rectangle in

two ways.

x 5

3

x

Page 7: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

54

54

5.7 – Dividing Polynomials

A. Dividing by a monomial

Create separate fractions and then simplify

each separately.

1. 10π‘₯4𝑦3+15π‘₯2𝑦8

10π‘₯2𝑦9

2. (8π‘₯3𝑦 βˆ’ 4π‘₯7𝑦5 + 2π‘₯2𝑦4) Γ· (4π‘₯𝑦8)

B. Dividing by a non-Monomial

Use long division.

Recall... 512 Γ· 31

3. (π‘₯3 + 4π‘₯2 βˆ’ 2π‘₯ + 8) Γ· (π‘₯ βˆ’ 1)

4. 4𝑑3+4𝑑2βˆ’9𝑑+3

2𝑑+3

Page 8: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

55

55

5. (4π‘₯3 + 5π‘₯ βˆ’ 12) Γ· (2π‘₯ βˆ’ 3)

6. (π‘₯3 βˆ’ 27) Γ· (π‘₯ βˆ’ 3)

7. (𝑝4 βˆ’ 𝑝3 βˆ’ 4𝑝2 βˆ’ 2𝑝 βˆ’ 15) Γ· (𝑝2 + 2)

In Math 90, you will learn another method for

dividing called Synthetic Division. This process

will only work when dividing by a linear factor

(those without exponents). Problems like #7

above cannot be done using synthetic division

since there is an exponent in the divisor.

Page 9: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

56

56

6.1 – Introduction to Factoring

Factoring is _______________________ .

Factoring is a ________________ process.

A. Factoring Out a Greatest Common Factor

*Factor each of the following completely.

1. 24π‘₯ βˆ’ 36

2. 18π‘₯2 βˆ’ 18π‘₯

3. 20π‘₯5𝑦3𝑧2 βˆ’ 24π‘₯2𝑦5𝑧

4. 14π‘₯5𝑦3 βˆ’ 28π‘₯7𝑦2 + 35π‘₯2𝑦8

5. βˆ’12π‘₯3 + 4π‘₯2 βˆ’ 9

B. Factoring by Grouping

6. π‘₯2(π‘₯ βˆ’ 5) + 7(π‘₯ βˆ’ 5)

7. 5π‘₯(π‘₯3 + 2) βˆ’ 8(π‘₯3 + 2)

8. 3π‘ž + 3𝑝 + π‘žπ‘Ÿ + π‘π‘Ÿ

9. 8𝑀5 + 12𝑀2 βˆ’ 10𝑀3 βˆ’ 15

10. 2𝑐 + 3π‘Žπ‘¦ + π‘Žπ‘ + 6𝑦

Page 10: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

57

57

11. 12π‘₯2 + 6π‘₯ + 8π‘₯ + 4

12. 6𝑓2π‘˜ + 30π‘˜ + 2𝑓2 + 10

Review

1. Multiply: (π‘₯ + 1)(π‘₯ + 2)(π‘₯ + 3)

2. Simplify: 53

5βˆ’8

3. Simplify: (5π‘₯3𝑦2)βˆ’2

4. Simplify: (4π‘₯βˆ’3𝑦

6π‘₯π‘¦βˆ’5)βˆ’3

5. Multiply: (5.6 x 1014) (3.0 x 1022

)

6. Multiply: βˆ’4π‘₯2𝑦3𝑧(8π‘₯𝑦5 βˆ’ 11π‘₯2𝑧3)

7. Multiply: (5π‘₯2𝑦 βˆ’ 8𝑧)2

Page 11: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

58

58

8. Divide:

(16π‘₯4𝑦2 + 20π‘₯5𝑦 βˆ’ 24π‘₯3𝑦8) Γ· (6π‘₯2𝑦7)

9. Divide: (π‘₯3 + 6π‘₯ βˆ’ 7) Γ· (π‘₯ + 1)

10. Divide: (π‘š3 βˆ’ 64) Γ· (π‘š βˆ’ 4)

11. Factor: βˆ’8π‘₯3 + 16π‘₯2 + 20π‘₯

12. Factor: 5π‘₯2(π‘₯ + 7) βˆ’ 8(π‘₯ + 7)

13. Factor: 2𝑐 + π‘Žπ‘ + 3π‘Žπ‘¦ + 6𝑦

14. Factor: π‘₯𝑦 βˆ’ π‘₯𝑧 + 7𝑦 βˆ’ 7𝑧

15. Factor: 4π‘₯3 + 3π‘₯2𝑦 + 4π‘₯𝑦2 + 3𝑦3

Page 12: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

59

59

6.2 – Factoring Trinomials, part 1

* Factor each of the following:

1. π‘₯2 + 10π‘₯ + 16

2. π‘₯2 βˆ’ 3π‘₯ βˆ’ 18

3. π‘₯2 + 6π‘₯ βˆ’ 40

4. π‘š2 βˆ’ 12π‘š + 11

5. 𝑛2 + 8𝑛 + 16

6. 𝑀2 βˆ’ 7𝑀 + 12

7. 12𝑝2 βˆ’ 96𝑝 + 84

8. π‘₯3𝑦3 βˆ’ 19π‘₯2𝑦3 + 60π‘₯𝑦3

9. βˆ’2π‘š2 + 22π‘š βˆ’ 20

10. 5𝑀2 βˆ’ 40𝑀 βˆ’ 45

Page 13: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

60

60

6.3 – Factoring Trinomials, part 2

pattern: π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐

*Factor each of the following completely.

1. 3π‘₯2 + 13π‘₯ + 4

2. 7𝑦2 + 9𝑦 βˆ’ 10

3. 8 + 7π‘₯2 βˆ’ 18π‘₯

4. 12𝑐2 βˆ’ 5𝑐 βˆ’ 2

5. 12𝑦2 βˆ’ 73𝑦𝑧 + 6𝑧2

6. 36π‘₯2 βˆ’ 18π‘₯ βˆ’ 4

7. 12π‘š2 + 11π‘šπ‘› βˆ’ 5𝑛2

8. 𝑦2 βˆ’ 6𝑦 βˆ’ 40

9. 16π‘₯2 + 24π‘₯ + 9

10. 6𝑝4 + 17𝑝2 + 10

11. 3𝑦3 βˆ’ 𝑦2 + 12𝑦

Page 14: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

61

61

6.4 – Factoring Trinomials, part 3

The a-c Method

1. 6π‘₯2 + 7π‘₯ βˆ’ 3

2. 9π‘₯2 βˆ’ 12π‘₯ + 4

3. 16π‘₯2 + 10π‘₯ + 1

4. 16π‘₯2 βˆ’ 34π‘₯ βˆ’ 15

Page 15: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

62

62

6.5 – The Difference of Two Squares and Perfect Square Trinomials

The Difference of Two Squares

*Factor each completely:

1. π‘₯2 βˆ’ 49

2. π‘₯2 βˆ’ 64

3. π‘₯2 βˆ’ 25 4. π‘₯2 βˆ’ 10

5. π‘₯2 βˆ’1

36 6. π‘₯2 + 25

7. π‘₯2𝑦2 βˆ’ 100𝑧2

8. π‘₯4 βˆ’ 16

9. π‘₯8 βˆ’ 𝑦8

10. π‘₯2 βˆ’ 1 11. 25π‘₯2 βˆ’ 16

12. 100π‘₯2 βˆ’ 49𝑦2

13. 25π‘₯2 βˆ’ 100

14. π‘₯2 βˆ’ 6π‘₯𝑦 + 9𝑦2 βˆ’ 16

Page 16: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

63

63

15. π‘₯2 + 8π‘₯ + 16 βˆ’ 25𝑦2

16. 𝑀2 βˆ’ 10𝑀 + 25 βˆ’ 36π‘ž2

17. 100 βˆ’ π‘₯2 βˆ’ 16π‘₯𝑦 βˆ’ 64𝑦2

6.6 – The Sum & Difference of Two Cubes

Memorize:

π‘Ž3 + 𝑏3 = (π‘Ž + 𝑏)(π‘Ž2 βˆ’ π‘Žπ‘ + 𝑏2)

π‘Ž3 βˆ’ 𝑏3 = (π‘Ž βˆ’ 𝑏)(π‘Ž2 + π‘Žπ‘ + 𝑏2)

"SOAP" means....

*Factor each completely:

1. π‘₯3 + 125

2. 𝑦3 βˆ’ 64

3. 8π‘₯3 βˆ’ 1

4. 3π‘₯3 + 81

What if you forget these formulas?

Page 17: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

64

64

A General Stategy for Factoring

1. Can I factor out a _______________ ?

2. How many terms are there?

a. if four, try ____________________.

b. If three, try ____________________.

c. If two, try ______________________

or try _________________________.

3. Can I factor further?

The following exercises are from pages 470-471

of your textbook, which are printed on the next

page for your use.

#5. 2π‘Ž2 βˆ’ 162

#15. 3π‘ž2 βˆ’ 9π‘ž βˆ’ 12

#25. 64 + 16π‘˜ + π‘˜2

#10. 5π‘Ÿ3 + 5

#30. 3𝑦2 + 𝑦 + 1

#35. βˆ’π‘3 βˆ’ 5𝑝2 βˆ’ 4𝑝

#45. 14𝑒2 βˆ’ 11𝑒𝑣 + 2𝑣2

#55. 81𝑒2 βˆ’ 90𝑒𝑣 + 25𝑣2

#65. 12π‘₯2 βˆ’ 12π‘₯ + 3

Page 18: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

65

65

Page 19: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

66

66

6.7 – Solving Equations Using the Zero Product Rule

Quadratic equations are of the form

Zero Product Rule:

If 𝐴 βˆ™ 𝐡 = 0, Then 𝐴 = 0 π‘œπ‘Ÿ 𝐡 = 0.

Solve each of the following equations.

1. (π‘₯ + 2)(π‘₯ βˆ’ 3) = 0

2. (π‘₯ + 5)(2π‘₯ βˆ’ 3) = 0

3. (8π‘₯ βˆ’ 5)(7π‘₯ + 2) = 0

4. 1

3𝑧 (𝑧 βˆ’

5

8) = 0

5. π‘₯2 βˆ’ 2π‘₯ βˆ’ 15 = 0

6. π‘₯2 βˆ’ 8π‘₯ + 16 = 0

7. π‘₯2 βˆ’ 24 = 2π‘₯

8. π‘₯2 βˆ’ 25 = 0

9. 2π‘₯2 βˆ’ 50 = 0

10. π‘₯3 βˆ’ 25π‘₯ = 0

11. 2π‘₯3 βˆ’ 50π‘₯ = 0

Page 20: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

67

67

6.7 #26 𝑦2 βˆ’ 7𝑦 βˆ’ 8 = 0

6.7 #28 𝑀2 βˆ’ 10𝑀 + 16 = 0

6.7 #30 4π‘₯2 βˆ’ 11π‘₯ = 3

6.7 #35 2π‘š3 βˆ’ 5π‘š2 βˆ’ 12π‘š = 0

6.7 #38 4(2π‘₯ βˆ’ 1)(π‘₯ βˆ’ 10)(π‘₯ + 7) = 0

6.7 #46 2𝑦2 βˆ’ 20𝑦 = 0

6.7 #48 9𝑛2 = 1

6.7 #49 2𝑦3 + 14𝑦2 = βˆ’20𝑦

6.7 #62 3𝑧(𝑧 βˆ’ 2) βˆ’ 𝑧 = 3𝑧2 + 4

6.7 #69 (π‘₯ βˆ’ 1)(π‘₯ + 2) = 18

Page 21: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

68

68

6.8 – Quadratic Word Problems

A. Number Problems

6.8 #10 If a number is added to two times its

square, the result is 36. Find all such numbers.

B. Consecutive Integer Problems

Review...

Consecutive Integers

Consecutive Even Integers

Consecutive Odd Integers

6.8 #14 The product of two even consecutive

integers is 48. Find all such numbers.

6.8 #16 The sum of the squares of two

consecutive integers is 9 less than 10 times their

sum. Find all such integers.

The product of two consecutive odd integers is

63. Find all such integers.

Page 22: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

69

69

The perimeter of a rectangle is 22 cm and its

area is 24cm2. Find the length and width of this

rectangle.

C. Area Problems

6.8 #18 The width of a rectangular picture frame

is 2 inches less than its length. The area is 120 in2.

Find its dimensions.

The length of a rectangle is three times its

width. Find the dimensions if the area is 48

cm2.

D. Height of a Projectile

6.8 #26 A stone is dropped off a 256-ft. cliff. The

height of the stone is given by β„Ž = βˆ’16𝑑2 + 256,

where t is the time (in seconds). When will it hit the

ground?

Page 23: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

70

70

E. The Pythagorean Theorem

Find x:

6.8 #42 The longer leg of a right triangle is 1 cm

less than twice the shorter leg. The hypotenuse is 1

cm more than twice the shorter leg. Find the length

of the shorter leg.

Review of Chapters 5 & 6

1. Simplify: (5π‘₯2𝑦)(βˆ’3π‘₯4𝑦3)

2. Simplify: 5π‘₯0

3. Simplify: 3βˆ’3

4. Simplify: (π‘₯5)3

5. Simlify: (3π‘₯βˆ’2𝑦4

6π‘₯5π‘¦βˆ’2)βˆ’3

6. Simplify: (βˆ’4π‘₯βˆ’5π‘¦βˆ’3𝑧

8π‘₯βˆ’7𝑦4π‘§βˆ’3 )βˆ’4

8

10 x

Page 24: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

71

71

7. Write 5.37 x 104 in standard form.

8. Write 365,000,000 in scientific notation.

9. Multiply: (3.5 x 1011) (4.0 x 1023

)

10. Divide: 6.0 x 104

8.0 x 1023

11. Divide: π‘₯3+64

π‘₯+4

12. Divide:

(5π‘₯3 + 10π‘₯2 βˆ’ 15π‘₯ + 20) Γ· (15π‘₯3)

13. Simplify: (3π‘₯ βˆ’ 2𝑦)2

14. Add: (4π‘₯ + 2) + (3π‘₯ βˆ’ 1)

15. Subtract 3π‘₯2 βˆ’ 4π‘₯ + 8 from π‘₯2 βˆ’ 9π‘₯ βˆ’ 11.

16. Multiply: (3π‘₯ + 5)(2π‘₯ βˆ’ 7)

17. Multiply: (π‘₯ βˆ’ 4)(π‘₯2 + 5π‘₯ βˆ’ 3)

Page 25: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

72

72

18. The square of a number is subtracted from

60, resulting in βˆ’4. Find all such numbers.

19. The product of consecutive integers is 44

more than 14 times their sum. Find all such

integers.

20. The length of a rectangle is 1 ft. longer than

twice its width. If the area is 78 ft2, find the

rectangle's deimensions.

21. A right triangle has one leg that is 2 ft.

longer than the other leg. The hypotenuse is 2

ft. less than twice the shorter leg. Find the

lengths of all three sides of hte triangle.

Page 26: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

73

73

22. Factor: π‘₯2 + π‘₯ βˆ’ 42

23. Factor: 𝑐4 βˆ’ 1

24. Factor: βˆ’10𝑒2 + 30𝑒 βˆ’ 20

25. Factor: 𝑦3 βˆ’ 125

26. Factor: 49 + 𝑝2

27. Factor: 2π‘₯3 + π‘₯2 βˆ’ 8π‘₯ βˆ’ 4

28. Factor: 3π‘Ž2 + 27π‘Žπ‘ + 54𝑏2

Page 27: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

74

74

Additional Review (Chapters 5&6) – If Time

1. Write 463,000,000 in scientific notation.

2. Multiply: (2.5 x 1017) (6.0 x 10βˆ’4

)

3. Divide: 6.0 π‘₯ 10βˆ’4

8.0 π‘₯ 1019

4. Simplify each:

a. 5π‘₯0

b. (5π‘₯)0

c. (βˆ’2

3)

2

d. βˆ’8βˆ’2

e. (βˆ’8)βˆ’2

f. (βˆ’3π‘š2𝑛3)4

g. βˆ’5π‘₯βˆ’2𝑦3

βˆ’10π‘₯4π‘¦βˆ’5

h. (βˆ’3π‘’βˆ’2𝑣

π‘€βˆ’3 )βˆ’2

βˆ™ (π‘’π‘£βˆ’2)

5. Given 5π‘₯2 + 3π‘₯7 βˆ’ 2π‘₯ + 8, state find each:

a. Leading coefficient: ___________

b. degree of the polynomial: ___________

6. Find the degree of the polynomial:

π‘₯2𝑦4𝑧 + 3π‘₯𝑦7𝑧2 βˆ’ 2π‘₯4𝑦𝑧3

Page 28: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

75

75

7. Add: (2π‘₯ βˆ’ 5) + (4π‘₯ + 8)

8. Combine:

(π‘₯2 + 4π‘₯ βˆ’ 9) βˆ’ (2π‘₯2 βˆ’ 3π‘₯ + 4) + (5π‘₯2 βˆ’ 11)

9. Multiply each:

a. (3π‘₯ βˆ’ 5)(2π‘₯ + 7)

b. (4π‘₯ + 7)(4π‘₯ βˆ’ 7)

c. (3π‘₯ + 2𝑦)(4π‘₯ βˆ’ 9𝑦)

d. (5π‘₯ βˆ’ 8)2

e. (π‘₯ + 5)(π‘₯2 βˆ’ π‘₯ + 2)

10. Divide: 5π‘₯2𝑦3βˆ’12π‘₯𝑦4+10π‘₯4𝑦

8π‘₯3𝑦2

11. Divide: (6π‘₯2 βˆ’ 5π‘₯ + 4) Γ· (π‘₯ βˆ’ 3)

12. Factor: 5π‘₯2 + 10π‘₯ + 100

13. Factor: 60π‘₯π‘Ž βˆ’ 30π‘₯𝑏 βˆ’ 80π‘¦π‘Ž + 40𝑦𝑏

Page 29: 5.1, 5.2, 5.3 Properites of Exponentsvvcforme.com/math-videos/a/Lecture_Guide 42_ch5-6.pdfbinomial trinomial polynomial *Find the perimeter: Vocabulary: 𝑛+ π‘›βˆ’1+β‹―+ + *Given:

76

76

14. Factor: π‘₯2 βˆ’ 3π‘₯ βˆ’ 28

15. Solve: π‘₯2 βˆ’ 3π‘₯ βˆ’ 28 = 0

16. Factor: 2π‘₯2 βˆ’ π‘₯ βˆ’ 6

17. Factor: π‘₯4 βˆ’ 16

18. Factor: π‘₯3 βˆ’ 27𝑦3

19. Solve: π‘₯2 = 8π‘₯

20. The length of a rectangle is 2 cm more than

three times its width. Find the dimensions if

the area is 56 cm2.