ALGEBRA 2 - cs.stcc.eduHomework List 097/099 Introductory Algebra through Applications Workbook You will find the problems under Additional Exercises Chapter 6 6.1 p. 175 – 176 #

ALGEBRA 2

Prepared by Nicole Bedinelli

2016

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3

Course Outline

Chapter 6A: Factoring Polynomials6.1 Common Factors6.2 Factoring Trinomials with Coefficient of One6.3 Factoring Trinomials with Coefficient Other than OneQuiz 206A

Chapter 6B: Factoring Polynomials6.4 Factoring Perfect Square Trinomials and Difference of Squares6.5 Solving Quadratic Equations by FactoringQuiz 206B

Exam 1 – Test Code 791 – Chapter 6

Chapter 7A: Rational Expressions and Equations7.1 Rational Expressions7.2 Multiplication and Division of Rational ExpressionsQuiz 207A

Chapter 7B: Rational Expressions and Equations7.3 Addition and Subtraction of Rational Expressions7.4 Complex Rational ExpressionsQuiz 207B

Chapter 7C: Rational Expressions and Equations7.5 Solving Rational Expressions7.6 Ratio and ProportionQuiz 207C

Exam 2 – Test Code 792 – Chapter 7

Chapter 8A: Radical Expressions and Equations8.1 Introduction to Radical Expressions8.2 Addition and Subtraction of Radical ExpressionsQuiz 208A

Chapter 8B: Radical Expressions and Equations8.3 Multiplication and Division of Radical Expressions8.4 Solving Radical ExpressionsQuiz 208B

Chapter 9A: Quadratic Equations9.1 Solving Quadratic Equations by the Square Root Property9.3 Solving Quadratic Equations Using the Quadratic FormulaQuiz 209A

Chapter 9B: Quadratic Equations9.1 Graphing Quadratic EquationsQuiz 209B

Final Examination – Test Code 793This final examination is comprehensive, including all units covered this semester.

4

Homework List 097/099

Introductory Algebra through Applications Workbook

You will find the problems under Additional Exercises

Chapter 6

6.1 p. 175 – 176 # 2, 4, 5, 8, 11, 12

6.2 p. 178 – 179 # 3, 5, 6, 9, 14, 18

6.3 p. 182 – 183 # 1, 2, 3, 4, 5, 6

Quiz 206A

6.4 p. 187 – 189 # 5, 6, 8, 13, 14, 17, 19

6.5 p. 194 – 196 # 3, 4, 5, 7, 10, 12, 14, 16, 18, 21

Quiz 206B

Exam 1 791 (Based on chapter 6)

Chapter 7

7.1 p. 199 – 201 # 1, 2, 4, 8, 10, 11, 12, 13, 14, 15, 17

7.2 p. 204 – 207 # 1, 3, 5, 8, 9, 11, 12, 14, 17

Quiz 207A

7.3 p. 211 – 213 # 1, 2, 5, 6, 14, 15, 17

7.4 p. 217 – 219 # 1, 4, 7, 8, 9, 11

Quiz 207B

7.5 p. 223 – 226 # 1, 3, 4, 5, 10, 11, 14, 16

7.6 p. 228 – 230 # 2, 5, 7, 8, 11, 12, 13

Quiz 207C

Exam 2 792 (Based on Chapter 7)

Chapter 8

8.1 p. 233 – 234 # 1 – 18

8.2 p. 236 – 238 # 1, 2, 3, 4, 6, 8, 9, 10, 13, 16

Quiz 208A

8.3 p. 241 – 244 # 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 16, 18, 19, 20, 21, 22

8.4 p. 247 – 250 # 1, 2, 3, 5, 6, 8, 12, 16

Quiz 208B

Chapter 9

9.1 p. 253 – 254 # 1, 4, 6, 8, 13, 15, 17, 18

9.3 p. 262 – 264 # 1, 3, 5, 7, 9, 11, 13, 15

Quiz 209A

9.4 p. 270 – 272 # 3, 4, 6, 8, 9, 11

Quiz 209B

Exam 3 793 ( Cumulative Final)

5

Chapter 6 Factoring Polynomials

6.1 Greatest Common Factor: GCF

List all the factors of the following numbers:

20 30

Which is the largest factor the two numbers have in common? Or the GCF.

Find the GCF.

Ex. 1. 40, 100 Ex. 2. 12, 16

GCF of monomials.

2x3 , and 8x5 The GCF of the coefficients 2 and 8 is 2.

Both terms have 3 factors of x in common.

So the GCF is 2x3

Find the GCF.

Ex. 1. x3, x4, x7 Ex. 2. 12x2, -16x3

6

Ex. 3. 3y6, 5y3 Ex. 4. 24x5y6, 8x4y4

To factor the GCF out of a polynomial, is to reverse the process of multiplication.

Multiply 2x(x2 + 2x – 3) Factor 2x3 + 4x2 – 6x

2x3 + 4x2 – 6x 2x( x2 + 2x – 3)

Factor the polynomial.

3x + 6 First find the GCF of the two terms 3x, and 6.

The GCF is 3. Divide each term by the GCF.� �

�+

�

�

3(x + 2)

Check by multiplying 3(x + 2) = 3x + 6

Factor Completely.

Ex. 1. 2x3 + 10x2 + 8x Ex. 2. x2 + 3x

Ex. 3. 84x2 – 56x + 28 Ex. 4. 3x4 – x2

Ex. 5. 2x – x2 + x Ex. 6. 14x3 – 7x2

7

6.1 Classwork

Find the GCF

1. 8x4 , -24x2 2. –x2, -6x, -24x5

3. 8x2, -4x, 20 4. 2x2y, 4xy, 6x3y2

Factor. Check by multiplying.

5. z2- z 6. 8x4 – 24x2

7. 8x2- 4x – 20 8. 6x4 – 10x3 - 3x2

9. 8y3 – 20y2 + 12y – 16 10. x5y5 + x4y3 + x3y3 – x2y2

8

6.2 Factoring Trinomials whose leading Coefficients is 1

This is reverse FOIL

(x + 2)(x + 3) = x2 + 3x + 2x + 6 = x2 + 5x + 6

x2+ 5x + 6 = ( x + 2)(x + 3) two numbers whose product is 6 and sum is 5

2 and 3

First follow the sign chart.

x2 + bx + c = (x + )(x + ) two numbers whose product is c, and sum is b

x2 – bx + c = (x - )(x - ) two numbers whose product is c and sum is b

x2 – bx – c = (x - )( x + ) two numbers whose product is c, and difference is b

* the larger absolute value number is the negative

x2 + bx – c = (x - )(x + ) two numbers whose product is c, and difference is b

* the larger absolute value number is positive

Using the chart, factor the following trinomials.

x2 + 7x + 10 so we need 2 numbers whose product is 10, and sum is 7

(x + )(x + ) using the sign chart, we know our binomials are both positive

x2 + 7x + 10 = (x + 5)(x + 2) * it does not matter which order the binomials are in

Check with FOIL (x + 5)(x + 2) = x2 + 2x + 5x + 10 = x2 + 7x + 10

9

Factor the trinomials.

Ex. 1. x2 – 10x + 16 Ex. 2. x2 + 5x + 4

Ex. 3. x2 – 3x – 18 Ex. 4. y2 – 3y – 4

Ex. 5. x2 + 4x – 45 Ex. 6. t2 + t – 6

Ex. 7. x2 + 6x + 4 Ex. 8. 2x2 – 10x – 48

Ex. 9. – 9x + x2 + 14 Ex. 10. –x2 – 10x + 11

10

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6.2 Classwork Factoring Trinomials (a = 1)

Factor each completely.

1)

b2 + 8

b + 7 2)

n2 − 11

n + 10

3)

m2 +

m − 90 4)

n2 + 4

n − 12

5)

n2 − 10

n + 9 6)

b2 + 16

b + 64

7)

m2 + 2

m − 24 8)

x2 − 4

x + 24

9)

k2 − 13

k + 40 10)

a2 + 11

a + 18

11)

n2 −

n − 56 12)

n2 − 5

n + 6

-1-

11

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13)

b2 − 6

b + 8 14)

n2 + 6

n + 8

15)

2

n2 + 6

n − 108 16)

5

n2 + 10

n + 20

17)

2

k2 + 22

k + 60 18)

a2 −

a − 90

19)

p2 + 11

p + 10 20)

5

v2 − 30

v + 40

21)

2

p2 + 2

p − 4 22)

4

v2 − 4

v − 8

23)

x2 − 15

x + 50 24)

v2 − 7

v + 10

25)

p2 + 3

p − 18 26)

6

v2 + 66

v + 60

-2-

12

6.3 Factoring Trinomials with Leading Coefficient Other than One

Factoring ax2 + bx + c, where a ≠ 1

4x2 + 7x + 3 we see a = 4, b = 7, and c = 3

list all the factor groups of a and c, to get a sum of b

4 3 you need a combination that adds to 7, after you multiply across

4 3 3

1 1 4 3 + 4 = 7

2

2

Using the same sign chart as before, we have to set up the binomials.

4 3

1 1 we use the opposite of what is being multiplied

and the “a” factor is always the first in the parenthesis

So… (4x + 3)(x + 1) check by FOIL

(4x + 3)(x + 1) = 4x2 + 4x + 3x + 3 = 4x2 + 7x + 3

Factor.

3x2 – 5x – 2 need factors of 3 and 2, and a difference of 5

3 2

3 2

1 1

Since there are two possible choices, we use FOIL to find the correct one.

13

Ex. 1. 2x2 + 7x + 3 Ex. 2. 2x2 + 23x + 56

Ex. 3. 7x2 – 11x – 6 Ex. 4. 12x2 – 4x – 1

Ex. 5. 20x2 – 3x - 2 Ex. 5. 2x2 – 3x – 5

14

6.3 Classwork Factor

1. 3x2 – 5x + 2 2. 6x2 + 5x + 1

3. 5x2 – x – 18 4. 2x2 + 3x – 5

5. 4x2 + 5x + 1 6. 4x2 – 3x + 1

7. 2x2 + 3x – 5 8. 6x2 – x – 2

15

6.4 Factoring Trinomial Squares and Difference of Squares

Trinomial squares x2 + 8x + 16 = (x + 4)(x + 4) = (x + 4)2

x2 – 12x + 36 = (x – 6)(x – 6) = (x – 6)2

Ex. 1. x2 – 6x + 9 Ex. 2. 2x2 – 20x + 50

Ex. 3. x2 + 18x + 81 Ex. 4. -12x + 36 + x2

Difference of squares a2 – b2 = (a – b )(a + b)

x2 – 4 = (x – 2)(x + 2) *only two terms, both perfect squares,

be a difference

4x2 – 9 = (2x + 3)(2x – 3)

Ex. 1. y2 – 36 Ex.2. 16x4 – 49

16

Ex. 3. x2 – 15 Ex. 4. 49 – 25t2

Ex. 5. 64 – x2 Ex. 6. 9w2 – 1

Ex. 7. 81x4 – 1 Ex. 8. p4 – 16

Ex. 9. x2 + 4 Ex. 10. 5 – 20x2

Factor Completely.

Ex. 1. 49c2 – d2 Ex. 2. 50x – 18x3

Ex. 3. 8x3 – 56x2 + 98x Ex. 4. 3x4 – 3

17

6.4 Classwork

Factor completely. Remember to look first for a common factor.

1. x2 + 4x + 4 2. x2 + 20x + 100

3. 2x2 – 40x + 200 4. 64 – 16x + x2

5. p2 – 16 6. 4x2 – 25y2

7. 16a2 – 9 8. 24x2 – 54

9. y4 – 1 10. 5x2 - 405

18

6.5 Solving Quadratic Equations by Factoring

Quadratic Equation ax2 + bx + c = 0 , a≠ 0

Principle of Zero Product (x + 3)(x – 2) = 0

x + 3 = 0 x – 2 = 0 set them equal to zero and solve

-3 -3 +2 +2

x = -3 x = 2

two solutions make this true, let’s check

Use the principle of zero product to solve the already factored equations.

Ex. 1. (x + 1)(x – 7) = 0 Ex. 2. x(4x – 7) = 0 Ex. 3. (2x – 1)(3x + 4) = 0

Use factoring to solve the quadratic equations.

x2 – 5x – 6 = 0 1. Set the equation equal to zero

(x – 6)(x+ 1) = 0 2. Factor

x – 6 = 0 x + 1 = 0 3. Set them equal to zero separate and solve

+6 +6 -1 -1 *(principle of zero product)

x = 6 x = -1

so x = 6, -1 are both solutions to the equation

19

Solve by factoring.

Ex. 1. x2 + 5x + 4 = 0 Ex. 2. x2 – 4x = 0

Ex. 3. 12x2 + 6x = 0 Ex. 4. 4x2 – 8x + 12 = 0

Ex. 5. x2 – 16 = 0 Ex. 6. 4x2 – 9 = 0

Ex. 7. x 2 – 3x = 28 Ex. 8. 9x2 = 16

Ex. 9. -2x2 + 13x – 21 = 0 Ex. 10. x(x + 7) = 18

20

6.5 Classwork

Solve using the principle of zero products.

1. (x + 9)(x – 7) = 0 2. (2x – 4)(3x + 5) = 0 3. x(x – 10) = 0

Solve by factoring and using the principle of zero products.

4. x2 + 7x – 18 = 0 5. x2 – 8x = 0

6. x2 = 16 7. 0 = 25 + x2 + 10x

8. 3x2 – 7x = 20 9. 2y2 + 12y = -10

10. 12y2 – 5y = 2 11. x2 – 5x = 18 + 2x

21

Chapter 6 Applications 090

1. A rectangle has a length 4 more then it’s width. The area is 60ft2. Find the length.

2. Four times a number added to the square of a number is equal to 5. Find such

numbers.

3. If the area of a triangle is 81ft2, and the base is twice the height. What is the base

of the triangle?

4. The hypotenuse of a right triangle is 17m. One leg is 7 more then the other leg.

What is the length of the longer leg?

22

5. The area of a triangle is 72in2. The height is 7 more than the base. What is the

height?

6. Twelve more than the square of a number is seven times the number. Find all such

numbers.

7. A rectangle has a width that is seven feet less than the length. The area is 60ft2. Find

the width.

8. A right triangle has a leg of 8in. The hypotenuse is 4 more than the other leg. What is

the length of the hypotenuse?

23

7.1 Rational Expressions

A rational expressionP

Qis an algebraic expression that can be written as a quotient of

two polynomials, P and Q, where Q ¹ 0.

Identify all numbers for which the following rational expressions are undefined.

4

x - 2undefined is when the denominator is zero

So when x – 2 = 0

x = 2 the rational expression is undefined when x = 2

Ex. 1.3x

x + 4Ex. 2.

5x

2Ex. 3.

� �

� � � � � � �

Simplify3

6=

1

2

To simplify a rational expression - Factor the numerator and denominator

- Divide out all common factors

� � � �

� � �=

� �

� � � � �=

24

Ex. 1.� � � � �

� � � �= Ex. 2.

� � � �

� � � �=

Ex. 3.� � � �

� � � �= Ex. 4.

� � �

� � � �=

Ex. 5.� � � � �

� � � � � � �= Ex. 6.

� � �

� � �=

Ex. 7.� � � � �

� � �= Ex. 8.

� � � �

� � � � � � �=

25

7.1 Classwork

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Identify the values for which the rational expression is undefined.

1) r - 27A) r = 2 B) r = -2 C) r = 0 D) None

1)

2) y + 74y - 7

A) y = 4 B) y = 7 C) y = 74 D) y = -7

2)

3) 2y - 4y2 - 64A) y = 8 B) y = 8 or y = -8 C) y = 64 D) y = 2

3)

Simplify.

4) 10xy3xy

A) 103 B) 13 C) y3y D) 10x3x

4)

5) 18m4p2

2m10p

A) 9m6p2 B) 9m6

p C) 9mp D) 9pm6

5)

6) 16x2y5

12x3y5

A) 3x4 B) 43 C) 43x D) 4x3

6)

7) -7x - 288x + 32

A) - 79 B) - 7

8C) x + 4 D) -4

7)

26

8) a2 - 8a(a + 3)(a - 8)

A) aa + 3 B) a - 8

a + 3 C) 1a + 3 D) a2

a + 3

8)

9) m2 - 25m25 - mA) -m B) m + 5 C) m D) -m - 5

9)

10) 2x + 210x2 + 18x + 8

A) 2x5x + 4 B) 1

5x + 4

C) 2x + 210x2 + 18x + 8

D) 2x + 55x + 18

10)

27

7.2 Multiplying and Dividing Rational Expressions

2

5.5

8=

2

x.x

4=

So you factor both numerators and denominators, then divide out common factors.

Ex. 1.� �

� � �∙� �

� �= Ex. 2.

� � � �

� �∙�

� �=

Ex. 3.� �

� � � � �∙� � � � �

� �= Ex. 4.

� � � � � � �

� � � �∙� � � � � � �

� � � �=

Ex. 5.� � � � � � � �

� � � �∙� � � � � �

� � �= Ex. 6.

� � � � � � �

� � � � � � � �∙� � � � � � � �

� � � � � � � �=

28

To divide rational expressions, multiply by the reciprocal, factor all numerators and

denominators. Divide out all common factors.

� �

�÷

� � �

�=

� �

�∙

�

� � �=

�

� �

Ex. 1.� � � � �

� � � � � �÷

� � � � � �

� � � � �= Ex. 2.

� � �

� �÷

� � �

� �=

Ex. 3.� � � � � � �

� � � � �÷

� � � �

� �= Ex. 4.

� � � � � � � �

� � � � � � �÷

� � � � � � � � �

� � � � � � �=

29

7.2 Classwork

Name___________________________________


Multiply. Express the product in lowest terms.

1) 2x25

∙ 40x3

A) 16x B) 80x2

5x3C) x16 D) 16x

2

x3

1)

2) 2x2

3y2 ∙ 12y

6

x3

A) 8y4x B) 8y

3x C) xy

418 D) x

5y418

2)

3) 2p - 2p

∙ 5p2

8p - 8

A) 16p2 + 32p + 165p3

B) 10p3 - 10p2

8p2 - 8p

C) 45p D) 5p4

3)

4) k2 + 6k + 9k2 + 12k + 27

∙ k2 + 9kk2 - 2k - 15

A) k2 + 9kk - 5 B) k

k2 + 12k + 27C) kk - 5 D) 1

k - 5

4)

Divide. Express the quotient in lowest terms.

5) 2x25

÷ x315

A) x 6 B) x

537 C) 6

x D) 6x2

x3

5)

6) 4d4

k2 ÷ 2d

6

k5

A) k3

2d2B) k

2

d4C) 8d

6

k5D) 2k

3

d2

6)

30

7) 6z - y3x

÷ 4y - 24z3x - 18

A) 4x6 - x B) 6x C) 6 - x

4 D) 6 - x4x

7)

8) 7x + 74x + 4

÷ 14x + 14x + 1

A) 18 B) 14 C) 1x + 1 D) x + 1

8

8)

9) y2 - 14y + 48y2 - 64

÷ y2 - 9y2 - 5y - 24

A) (y - 6)(y - 8)(y + 8)(y - 3) B) (y + 6)(y - 8)

(y + 8)(y + 3) C) y + 6y + 3 D) y - 6

y - 3

9)

10) xx2 + 9x + 20

÷ x2 + 8xx2 + 12x + 32

A) xx + 4 B) x + 5 C) x + 8

x + 5 D) 1x + 5

10)

31

7.3 Addition and Subtraction of Rational Expressions

Like denominators.

1

5+

2

5=

3

5

Ex. 1.3

x - 1+

8

x - 1= Ex. 2.

3x

4y-

x

4y=

Ex. 3.2x 2 + 5x - 7

3x - 1+

7x 2 - 5x + 6

3x - 1= Ex. 4.

6t - 7

t - 1-

t - 2

t - 1=

The least common denominator of rational expressions.

1

2+

4

5=

5

10+

8

10=

13

10The LCD of 2 and 5 is 10.

The LCD of2

9a 2,and

1

12a 4

9a2 = 3 ×3 ×a ×a 12a 4 = 2 ×2 ×3 ×a ×a ×a ×a

The LCD is 2 ×2 ×3 ×3 ×a ×a ×a ×a = 36a 4

To find the LCD, factor each denominator completely. Then use each factor the greatest

number of times it occurs in any of the denominators.

32

Find the LCD of each group of rational expressions.

Ex. 1.1

6and

2

nEx. 2.

1

10xand

7

12x 2

Ex. 3.1

tand

3

t + 1Ex. 4.

4x + 3

3x 2 - 3xand

x - 6

x 2 - 2x + 1

Ex. 5.7p + 1

p + 2and

5p

p - 1Ex. 6.

9n + 1

2n2 + 2nand

n - 5

n2 + 2n + 1

Adding and subtracting rational expressions with unlike denominators.

3

5x 2+

x + 1

6xy= The LCD of 5x2 and 6xy is 30x2y

6y

6y×

3

5x 2+

(x + 1)

6xy×5x

5xMultiply each fraction by the missing pieces

18y

30x 2y+

5x (x + 1)

30x 2yAdd the numerators, and simplify.

18y + 5x (x + 1)

30x 2y=

18y + 5x 2 + 5x

30x 2y

33

Add or subtract the rational expressions.

Ex. 1.1

2n-

3

5n= Ex. 2.

2

7p3+

p + 3

2p=

Ex. 3.x + 2

x-

x - 4

x + 3= Ex. 4.

9

2x + 4+

x

x 2 - 4=

Ex. 5.6

x - 1-

4

1 - x= Ex. 6.

3x - 4

x - 2+

x + 1

2 - x=

Ex. 7.y

y 2 + 5Y + 6-

4Y + 1

Y 2 + 3Y + 2= Ex. 8.

7n

n2 + 4n + 3-

3n - 2

n2 + 2n + 1=

34

7.3 Classwork

Name___________________________________

Perform the indicated operation or operations. Simplify, if possible.

1) 512 x

+ 212 x

1)

2) -30m - 6

+ 5mm - 6

2)

3) m2 - 7mm - 5

+ 10m - 5

3)

The following expressions represent denominators of rational expressions. Find their LCD.4) 2(a + 7 ) and 7(a + 7 )

A) 9(a + 7 ) B) 14(a + 7 )2 C) 9(a + 7 )2 D) 14(a + 7 )4)

5) n, 5 + n, and 5 - nA) n(5 + n)(5 - n) B) 25 - n2 C) 25n2 D) n2 + 25

5)

6) r2 + 6r + 9 and r2 + 3rA) r(r + 1)(r + 3) B) r(r + 3) C) r(r + 3)2 D) (r + 3)2

6)

Perform the indicated operation. Simplify, if possible.

7) 314c

+ 910c2

A) 1214c + 10c2

B) 3(5c + 21)70c2

C) 10870c2

D) 12140c2

7)

8) 5z2

- 3z

A) 5 - 3 zz2

B) 5 z + 3z2

C) 5 + 3 zz2

D) 3 z - 5z

8)

9) 6a + 7a - 9

A) 54a - 13a(a - 9) B) 13a - 54

a(a - 9) C) 13a - 54a(9 - a) D) 54a - 13

a(9 - a)

9)

35

10) 1x - 5

+ 45 - x

A) -3x - 5 B) 5

x - 5 C) 3x - 5 D) 4

x - 5

10)

11) 26x + 36

+ 118x + 180

A) 7x + 66(6x + 6)(3x + 10) B) -5x - 54

(6x + 6)(3x + 10)

C) 5x + 5418(x + 6)(x + 10) D) 7x + 66

18(x + 6)(x + 10)

11)

12) n + 1n2 + 4n + 4

+ n + 2n2 + 11n + 18

A) 6n + 5(n + 2)2(n + 9)

B) 2n2 + 14n - 13

(n + 2)2(n + 9)

C) 2n2 + 14n + 13

(n + 9)2(n + 2)D) 2n

2 + 14n + 13(n + 2)2(n + 9)

12)

13) 55 - y

- 2y - 5

A) 105 - y B) 7

5 - y C) -35 - y D) 3

5 - y

13)

14) 12xyx2 - y2

- x - yx + y

A) x2 + 10xy + y2(x + y)(x - y) B) x

2 + 14xy + y2(x + y)(x - y)

C) -x2 + 14xy - y2(x + y)(x - y) D) -x2 + 10xy - y2

(x + y)(x + y)

14)

15) 9xx2 - 5x + 6

- 36x2 - 6x + 8

A) x - 6(x - 3)(x - 4) B) 9(x - 6)

(x - 3)(x - 4)

C) 9(x - 2)(x - 3) D) 9x - 36

(x - 2)(x - 3)(x - 4)

15)

36

7.4 Complex Rational Expressions

1

3+

3

4

7

8-

5

6

Fractions on top of fractions. Need to find the LCD.

The LCD of 3, 4, 6, and 8 is 24. Multiply the numerator and

Denominator by the LCD.

24

1×1

3+

3

4×24

1

24

1×7

8-

5

6×24

1

=8 + 18

21 - 20=

26

1= 26

1. Find LCD

2. Multiply all terms in numerator and denominator by LCD to divide out fractions.

3. Simplify

Ex. 1.

x

2+

2x

3

1

x-

x

2

Ex. 2.

1 +1

x

1 -1

x 2

37

Ex. 3.

1

5-

1

a

(5 - a)

5

Ex. 4.x 2

1

x+

2

x 2

Ex. 5.

4

x

2

x 3

Ex. 6.

1

2a2-

1

2b2

5

a+

5

b

38

7.4 Classwork

Name___________________________________


Simplify.

1)

x9

2y7

x6

y3

A) x15

2y10B) x3

2y10C) x

3

2y4D) x

3

y4

1)

2)

4 + 2x

x4

+ 18

A) x16 B) 16 C) 16x D) 1

2)

3)

2x

+ 3y

3x

- 2y

A) x + yy - 1 B) 2y + 3x

3y - 2x C) y + xx D) -y

3)

4)

2x + 4yx

y3x2

+ 16

A) 12x B) 6x C) 12x(x2 + 2y)

(x2 + y)D) 12x

4)

5)

1a

+ 1

1a

- 1

A) 1 B) a1 - a2

C) 1 + a1 - a D) 1 - a2

5)

39

7.5 Solving Rational Equations

x

2+

x

6=

2

3choose LCD, 6

6

1×x

2+

6

1×x

6=

6

1×2

3multiply everything by LCD, divide out denominators

3x + x = 4 solve

4x

4=

4

4

x = 1

Ex. 1.4

n-

n + 1

3= 1 Ex. 2.

4

y + 2+

2

y - 1=

12

y 2 + y - 2

40

Ex. 3. x =9

x + 3+

3x

x + 3Ex. 4.

3

x-

1

x + 4=

5

x 2 + 4x

Ex. 5.4

5=

p

10Ex. 6.

2

y=

y - 4

16

Ex. 7.a

a + 3=

4

5aEx. 8.

4

w - 3=

7

w + 3

41

7.5 Classwork

Name___________________________________

Solve.

1) x5 - x9

= 2 1)

2) 4x - 2x

= 7 2)

3) 5 - xx

- 7x

= - 34 3)

4) 4x - 1

+ 42 x - 2

= 6 4)

5) 30x - 30x - 6

= 3x 5)

6) 6y + 5

- 4y - 5

= 12y2 - 25

6)

7) 91 = 36x 7)

8) 45 = 9x + 2 8)

9) x + 16

= 14x - 7 9)

10) 4x - 52x + 1

= 2x -1x + 6 10)

11) 2t = t3t - 4 11)

42

7.6 Applications

Ratios

A truck driver drives 60mi on 8 gal of gas. At the same rate, how many gallons of gas will

it take him to drive 120mi?

It would take Sue 1.5 hours to rake the leaves and it would take Bob 2hrs. How long would

it take if they worked together?

If 20 patients can be seen in 8 hours how many can be seen in 3?

43

Two brothers share a house. It would take the younger brother working alone 45 min to

clean the attic, where it would take the older brother 30 min. If the two brother worked

together, how long would it take them to clean the attic?

If it takes a painter 6 hrs to paint a room, and another worker it would take 4 hrs. How

long would it take if they worked together?

If a 16 pound turkey feeds 18 people how many people does a 4 pound turkey feed?

44

7.6 Classwork

Name___________________________________


Solve.1) Dr. Wong can see 8 patients in 2 hours. At this rate, how long would it take her to see 24patients?A) 5 hr B) 96 hr C) 16 hr D) 6 hr

1)

2) Maria and Charlie can deliver 90 papers in 3 hours. How long would it take them to deliver 39papers?A) 117 hr B) 6.9 hr C) 1.7 hr D) 1.3 hr

2)

3) If a boat uses 22 gallons of gas to go 71 miles, how many miles can the boat travel on 110 gallonsof gas?A) 375 miles B) 355 miles C) 710 miles D) 14 miles

3)

4) Martha can rake the leaves in her yard in 6 hours. Her younger brother can do the job in 7 hours.How long will it take them to do the job if they work together?

A) 1342 hr B) 7 hr C) 42 hr D) 4213 hr

4)

5) Frank can type a report in 3 hours and James takes 5 hours. How long will it take the two ofthem typing together?

A) 815 hr B) 5 hr C) 158 hr D) 152 hr

5)

6) Amy can clean the house in 8 hours. When she works together with Tom, the job takes 6 hours.How long would it take Tom, working by himself, to clean the house?

A) 25 hr B) 24 12 hr C) 2 hr D) 24 hr

6)

45

8.1 Introduction to Radical Expressions

A square root of a nonnegative real number a is a number that when squared is a.

The number under the radical sign is called the radicand.

r

Evaluate the following radical expressions.

Ex. 1. √25 Ex. 2. −√16 Ex. 3. √−4

Use a calculator to approximate the value of the irrational number to the nearest

thousandth.

Ex. 1. √10 Ex. 2. √2 Ex. 3.√�

�

Squaring a Square Root Taking the Square Root of a Square

(√ � ) � = � √ � � = �

Simplify each radical expression.

Ex. 1. (√49 ) � Ex. 2. (√2 ) � Ex. 3. √4� Ex. 4. √5�

Ex. 5. √100 � � Ex. 2. � 16 � � � � Ex. 3. − � 121 � � � � �

46

Simplify radical expression.

√24 = √4 ∙ 6 = 2√6 � 12 � � � � = � 4 ∙ 3 ∙ � � ∙ � ∙ � � ∙ � = 2� � � � � 3� �

Ex. 1. √72 Ex. 2. 2√40

Ex. 3. −4√27 Ex. 4. √20 � �

Ex. 5.√� �

� � �Ex. 6. 2√25� � � �

Ex. 7. ��

�Ex. 8. �

� �

� �

Ex. 9. ��

�Ex. 10. �

� � � � � �

�

47

8.1 Classwork

Name___________________________________

Find the value of the radical expression.1) 36

A) 8 B) 18 C) 12 D) 61)

2) - 49A) -7 B) -24.5 C) -14 D) 24.5

2)

3) 5 16A) -80 B) -20 C) 80 D) 20

3)

4) -5 100A) 500 B) -50 C) -500 D) 50

4)

Use a calculator to evaluate the radical expression, rounding to the nearest thousandth.5) 10

A) -3.286 B) 3.286 C) -3.162 D) 3.1625)

6) 5 10A) 15.840 B) -15.840 C) 15.811 D) -15.811

6)

Simplify.7) ( 64 )2

A) 8 B) 32 C) 16 D) 647)

8) 52

A) 25 B) 25 C) 5 D) 10 7

8)

9) 9x2A) 9x B) 3x C) 0 D) -3x

9)

10) x10y12

A) x5y12 B) x10y6 C) x8y10 D) x5y610)

Simplify. Assume that all variables and radicands represent nonnegative values.

11) t9

A) t9 t B) t18 t C) t4 t D) t5 t11)

12) 405 x8

A) 5 x4 9 B) 405 x4 C) 9 x4 5 D) 9 x8 512)

48

13) 72 x2

A) 72 x B) 2 x2 6 C) 6 x 2 D) 6 2 x

13)

14) 24 x2yA) 2 x 6 y B) 2 xy 6 C) 2 xy2 6 D) 2 x2 6 y

14)

Simplify.

15) 149

A) 25 B) 75 C) 17 D) 35

15)

16) 964

A) 1 B) 24 C) 83 D) 38

16)

17) 15r4

A) 15r B) 15

r4C) 15r4

r4D) 15

r2

17)

18) 75x2y49

A) x 75y7 B) 5x 3y

7 C) 5 3x2y7 D) 25x 3y

18)

19) 605x2

A) 605x B) 11 5

x C) 605x2

D) 55x

19)

20) 50yz2

x4

A) 5z 2yx2

B)5 2yz2

x2C) 25z 2y

x2D) z 50y

x2

20)

49

8.2 Addition and Subtraction of Radical Expressions

Like radicals are radical expressions that have the same radicand. Unlike radicals are

radical expressions with different radicands.

Adding like terms. Adding like radicals.

4x + 5x = 9x 4√2 + 5√2 = 9√2

Add or subtract.

Ex. 1. 5√3 − 2√3 Ex. 2. 7√ � – 2 √ � − 4√ �

Ex. 3. 4√ � − 1 − √ � − 1 Ex. 4. 3√6 + 2√2

Adding and Subtracting Unlike Terms.

√12 + √27 = √4 ∙ 3 + √9 ∙ 3 = 2√3 + 3√3 = 5√3 simplify, the collect like radicals

Ex. 1. 7√50 − √72 + √32 Ex. 2. −√4� + 3√ �

Ex. 3. −3√16� + √9� Ex. 4. 8√2 − √98

Ex. 5. √4� − 4 + √9� − 9 Ex. 6. √500 − 4√800

50

8.2 Classwork

Name___________________________________


Combine and simplify, if possible.1) 17 3 + 11 3

A) -29 3 B) -5 3 C) 6 3 D) 28 31)

2) -12 14 - 5 14A) -17 14 B) 8 14 C) -7 14 D) 16 14

2)

3) 12 10 - 8 10 - 10A) 5 10 B) -5 10 C) 3 10 D) 4 10

3)

4) -11 14x - 1 - 9 14x - 1A) -2 14x - 1 B) (-2x - 1) 14 C) (-20x - 1) 14 D) -20 14x - 1

4)

5) 4 7 + 3 175A) 7 7 B) 19 7 C) -19 7 D) 11 7

5)

6) 2 - 7 128 + 2 162A) -37 2 B) -5 292 C) -37 292 D) -5 2

6)

7) -4 125 - 9 245 - 4 20A) 510 5 B) -91 5 C) -4 5 D) -510 5

7)

8) 2 36y5 - 9y5

A) 15 y5 B) 9y2 C) 3y2 y D) 9y2 y

8)

9) 4x + 12 + x + 3A) 3x 3 B) 2 x + 3 C) 3 x + 3 D) 5x + 15

9)

10) 6 32x2 - 2 18x2 - 2x2

A) 4x 14 B) 3x 14 C) 17x 2 D) 18x 210)

51

8.3 Multiplication and Division of Radical Expressions

Multiply.

Ex. 1. √3 ∙ √5 Ex. 2. � −5√10 � � 6√2 � Ex. 3. √12 � � ∙ √3 �

Find the product. Simplify if possible. (Distribute)

Ex. 1. √8(2√3 + √2 ) Ex. 2. √� � 5 � � − 2 � Ex. 3. √6 � 3√3 − √8 �

Find the product. Simplify if Possible. (FOIL)

Ex. 1. � √� + 1 � (√� − 1) Ex. 2. � √� + 4 � � √� − 4 �

Ex. 3. (√3 + 2)� √3 − 2 � Ex. 4. (2√2 −3)� 2√2 + 3 �

52

Find the quotient and simplify.

Ex. 1.√ � �

√ �Ex. 2.

� � � � �

√ �Ex. 3.

� √ � � �

√ � � � �Ex. 4.

� � �

� � � � � �

Rationalizing the denominator. Rewrite the expression in an equivalent form that contains no

radical in its denominator.

�

√ �=

�

√ �∙√ �

√ �=

� √ �

√ � ∙√ �=

� √ �

�

Ex. 1.�

√ �Ex. 2.

�

√ �

Ex. 3. ��

� �Ex. 4. �

� �

�

Ex. 5. ��

� �Ex. 6. �

�

� �

53

8.3 Classwork

Name___________________________________


Multiply and simplify. Assume that all variables represent nonnegative numbers.1) p ∙ p3

A) p5 B) p2 C) p4 D) p2 p

1)

2) 2x6∙ 6x2

A) 2x8 3 B) 2x4 3 C) 4x4 3 D) 2 3x8

2)

3) 7 ( 3 - 5 )A) 21 - 35 B) 8 7C) 56 D) 7 3 + 7 5

3)

4) 13( 13 + 2)A) 195 B) 13 + 26 C) 39 D) 13 + 26

4)

Multiply, then simplify the product. Assume that all variables represent positive real numbers.5) ( 7 - 7)( 2 - 4)

A) -10 14 + 28 B) 14 + 28C) 14 - 4 7 - 7 2 + 28 D) 14 - 11 2 + 28

5)

6) (5 - 3 5)2

A) 25 - 9 5 B) 70 - 30 5 C) 25 + 9 5 D) 70 + 30 56)

7) ( 7 + 1)( 7 - 1)A) 6 - 2 7 B) 8 C) 6 + 2 7 D) 6

7)

8) ( 10 + 1)( 10 - 1)A) 9 B) 9 + 2 10 C) 9 - 2 10 D) 11

8)

Find the quotient and simplify, if possible.

9) 562

A) 2 B) 562 C) 2 7 D) 112

2

9)

10) 150x4

3x

A) 10x2 2x B) 5x2 2x C) 10x 2x D) 5x 2x

10)

54

11) 272

A) 2 B) 6 2 C) 16 D) 26

11)

Rationalize the denominator. Assume that all variables represent positive real numbers.

12) 423

A) 533 B) 4 23 C) 4 2323 D) 16 23

23

12)

13) 27

A) 51 B) 2 77 C) 2 7 D) 4 7

7

13)

14) 49 2

A) 7 2 B) 49 22 C) 11 D) 7 2

2

14)

15) 98x

A) 7xx B) 7 2x

x C) 7 2x D) 7 2x

15)

55

8.4 Solving Radical Equations

1. Isolate the radical.

2. Square each side of the Equation.

3. Solve and check.

√� − 2 = 5 check: √49 − 2 = 5+2 + 2 7 − 2 = 5

√� = 7 5 = 5

(√� )� = (7)�

� = 49

Ex. 1. � � + 3 = 7 Ex. 2. √� + 1 + 3 = 0

Ex. 3. � 2 � − 1 − 12 = −7 Ex. 4. √� + 8 = 0

Ex. 5. √2 � + 1 = √5 � − 2 Ex. 6. 1 + √1 − � = �

Ex. 7. 2√� + 6 = √� � + 19 Ex. 8. √3 � + 7 + 5 = 3 �

56

Applications.

Solve the following formulas for the indicated variable.

Ex. 1. � = ��

�solve for R Ex. 2. � = �

�

� �solve for S

Ex. 3. � = � � � solve for r Ex. 4. � = √� � + � � solve for w

Solve the following problems using the Pythagorean theorem. a2+b2=c2

Ex. 1 A 14 foot ladder is leaning against a house 11 ft up. How far away is the base of the ladder

from the house on the ground?

Ex. 2. The size of a TV is given by the length of the diagonal. What is the size of a TV whose

length is 16in and width is 9in?

57

8.4 Classwork

Name___________________________________


Solve and check.1) q + 4 = 5

A) 25 B) 21 C) 29 D) 811)

2) 7q - 6 = 6

A) 367 B) 6 C) 36 D) 30 7

2)

3) 4x - 10 - 7 = 0

A) 174 B) 49 C) No solution D) 594

3)

4) x + 5 = 0A) 5 B) 25 C) No solution D) -25

4)

5) 5x + 2 = 7A) 25 B) 5 C) 9 D) 1

5)

6) 7a - 2 = 5a + 7

A) 52 B) 912 C) 29 D) 92

6)

7) 2x + 15 - x = 6A) -7, -3 B) No solution C) -3 D) -7

7)

Solve the problem.

8) The period P of a pendulum in seconds is given by the formula P = 2! L19 , where L is the

length of the pendulum. Rewrite the formula by solving the equation for L.

A) L = ! 2 P B) L = 4 P2

19 !2C) L = 19 P

2

4 !2D) L = P 19

2!

8)

9) Given the area A of a circle, the formula r = A! can be used to calculate the radius of the

circle. Rewrite the formula by rationalizing the denominator on the right hand side.

A) r = !A!

B) r = ! A C) r = A!2

D) r = !AA

9)

58

Solve and check.10) The diagram below shows the side view of a plan for a slanted roof. Find the unknown length in

this roof plan.

?5 ft

8 ftA) 26 ft B) 3 10 ft C) 89 ft D) 13 ft

10)

Answer the question.11) The diagram below shows a rope connecting the top of a pole to the ground. The rope is 27 ydlong and touches the ground 13 yd from the pole.How tall is the pole? Express the answer as a simplified radical if the radicand is not a perfectsquare.

27 yd?

13 ydA) 562 yd B) 560 yd C) 4 35 yd D) 20 yd

11)

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.12) v2 = 2as for v

A) v = ± 2as

B) v = ±2a s C) v = ±2as D) v = ± 2as

12)

13) A = 13!r2 for r

A) r = ±3 A! B) r = ±A3! C) r = ± 3!

AD) r = ±

3A!

13)

59

9.1 & 9.3 Solving Quadratic Equations

Standard form of Quadratic Equations is: ax2 + bx + c = 0 where a≥ 1

Write the quadratic equation in standard form and identify a, b, and c.

Ex. 1. x2 + 3x – 2 = 0 Ex. 2. 2x – 3x2 = 6 Ex. 3. 4x2 = 4

Ex. 4. x2 = -5x Ex. 5. 16 = -5x2 + x Ex. 6. –x2 = 2x – 1

Solving quadratic equations. 1. Get the equation in standard form. (set equal to zero)

2. Factor to solve.

Ex. 1. x2 = 4x + 5 Ex. 2. 2x2 + 6x = -4

Ex. 3. 7x = 5x2 Ex. 4. 16 = x2

60

Solving Quadratic Equations Using the Quadratic formula.

ax2 + bx + c = 0 Quadratic formula � =� � ±√ � � � � � �

� �

2x2 + 3x – 5 = 0 � =� ( � )±� ( � )� � ( � )( � )( � � )

� ( � )

a = 2, b = 3, c = -5

� =� � ±√� � � �

�=

� � ±√� �

�=

� � ± �

�

so there are 2 solutions � =� � � �

�=

�

�= 1� =

� � � �

�=

� � �

�=

� �

�

Solve using the quadratic formula.

Ex. 1. x2 – 3x – 10 = 0 Ex. 2. x2 + 4x = 7

61

Ex. 3. x2 = x – 1 Ex. 4. 5x2 – 8x = 3

Ex. 5. x2 + 4x + 4 = 0 Ex. 6. 2x2 + 8x = -1

62

9.3 Solving Applications

Solve for c: E = mc2

Solve for t: � √ � = �

The width of a rectangle is 3 less than the length. If the area is 11 ft2, what is the length

and width?

63

An isosceles triangle has legs x cm, and a hypotenuse of 9cm. Find the length of the legs.

A triangle has a hypotenuse of 13in, and one leg is 2 in longer than the shorter leg. Find

the length of the legs.

64

9.1 Classwork

Name___________________________________


Rewrite the quadratic equation in the form ax2 + bx + c = 0, then identify a, b, and c.1) 4x2 = 9x

A) a = 4, b = -9, c = 0 B) a = 4, b = -9C) a = 3, b = 9, c = 0 D) a = 4, b = 0, c = 9

1)

2) 8x2 + 5 = 0A) a = 8, b = 0, c = 5 B) a = 2, b = 0, c = -5C) a = 0, b = 8, c = 5 D) a = 8, b = 5, c = 0

2)

3) 6x2 = 12x - 25A) a = 6, b = 12, c = 25 B) a = 6, b = 12, c = -25C) a = 6, b = -12, c = 25 D) a = 6, b = -12, c = -25

3)

4) -9x2 + 6x = 6A) a = 9, b = 6, c = -6 B) a = -9, b = 6, c = -6C) a = 9, b = 6, c = 6 D) a = -9, b = 6, c = 6

4)

5) (5x - 8)(x) = 7A) a = 5, b = -8, c = 7 B) a = 5, b = -8, c = -7C) a = -5, b = -8, c = -7 D) a = 5, b = 8, c = 7

5)

Solve.6) x2 = 64

A) 8 B) 8, -8 C) 9, -9 D) 326)

Solve using the quadratic formula.7) x2 - x = 6

A) -2, 3 B) 1, 6 C) 2, 3 D) -2, -37)

8) x2 + 2x - 120 = 0A) 12, -10 B) -12, 1 C) 12, 10 D) -12, 10

8)

9) 15x2 + 26x + 8 = 0

A) 25, 43

B) - 215, - 12

C) 25, - 43

D) - 25, - 43

9)

65

10) 5x2 + 10x + 2 = 0

A) -5 + 355

, -5 - 355

B) -5 + 155

, -5 - 155

C) -10 + 155

, -10 - 155

D) -5 + 1510

, -5 - 1510

10)

11) 4x2 = -12x - 2

A) -3 + 72

, -3 - 72

B) -3 + 112

, -3 - 112

C) -3 + 78

, -3 - 78

D) -12 + 72

, -12 - 72

11)

12) (5x - 9)(x + 1) = 0

A) 59, -1 B) 5

9, 1 C) 9

5, -1 D) 5

9, 0

12)

13) 3x(x - 3) = 2

A) - 53

B) 9 + 1056

, 9 - 1056

C) -9 + 1056

, -9 - 1056

D) - 35

13)

14) 4 = - 12x

- 4x2

A) -12 + 52

, -12 - 52

B) -3 + 132

, -3 - 132

C) -3 + 58

, -3 - 58

D) -3 + 52

, -3 - 52

14)

Solve the problem using the quadratic formula.15) The hypotenuse of a right triangle is 15 meters long. One leg is 3 meters longer than the other.

Find the lengths of the legs.A) 12 m, 18 m B) 6 m, 9 m C) 36 m, 39 m D) 9 m, 12 m

15)

16) The length of a rectangle is 7 cm greater than the width. The area is 228 cm2. Find the length andthe width.

A) 13 cm, 20 cm B) 12 cm, 19 cm

C) 14 cm, 21 cm D) 1072

cm, 1212

cm

16)

66

9.4 Graphing Quadratic Equations in Two Variables

A quadratic equation is a parabola that opens up, or down. This is determined by a.

y = ax2 + bx + c when a is positive it opens up

y = -ax2 + bx + c when a is negative, it opens down

Determine if the following graphs open up or down.

Ex. 1. y = 6x2 – 3x – 1 Ex. 2. y = x2 + 8 Ex. 3. y = -x2 – 2x

Ex. 4. y = -5x2 + x – 1 Ex. 5. y = -x2 Ex. 6. y = 2x2 + 3x – 2

Find the vertex of the parabola.

y = 2x2 + 4x + 1 a = 2, and b = 4

1. Find the x coordinate using� �

� �

� ( � )

� ( � )= −1

2. Find the y coordinate by evaluating the equation with the x coordinate:

y = 2x2 + 4x + 1 = 2(-1)2 + 4(-1) + 1 = 2 – 4 + 1 = -1

so the vertex is (-1, -1)

Find the vertex of the parabola.

Ex. 1. y = -2x2 – 8x + 18

67

Ex. 2. y = x2 – 6x – 7

Ex. 3. y = x2 + 16

Ex. 4. y = -5x2 + 20x

Graph y = x2 + 2x + 1

68

Find the x and y intercepts of the following quadratic equations.

Ex. 1. y = x2 + 4x + 4

Ex. 2. y = 3x2 – 5x

Ex. 3. y = x2 – 16

Ex. 4. y = x2 + 4x + 5

Ex. 5. y = 2x2 – 1x – 4

69

9.4 Claswork

Name___________________________________

Find the ordered pair for the vertex.1) y = x2 - 3

A) (3, 0) B) (-3, 0) C) (0, -3) D) (0, 3)1)

2) y = 4x2 + 40x + 103A) (3, -5) B) (-3, 5) C) (-5, 3) D) (5, -3)

2)

3) y = 3x2 + 30x + 76A) (1, -5) B) (-5, 1) C) (-1, 5) D) (5, -1)

3)

4) y = 2x2 + 20x + 53A) (5, -3) B) (-3, 5) C) (3, -5) D) (-5, 3)

4)

5) y = 4x2 + 24x + 40A) (4, -3) B) (-4, 3) C) (-3, 4) D) (3, -4)

5)

Determine if the graph opens up or down, and find the y-intercepts.6) y = -x2 + 2x - 2 6)

7) y = x2 + 5 7)

8) y = -x2 - 2 8)

9) y = 4x2 - 2x 9)

10) y = -3x2 + 5x 10)

Find the x-intercepts.11) x2 - 5x = 0 11)

12) x2 + 6x - 55 = 0 12)

13) 5x2 + 10x + 2 = 0 13)

70

ANSWERS CHAPTER 6

6.1 22. 4(v + 1)(v – 2) 5. x = 0, 8

23. (x – 10)(x – 5) 6. x = -4, 4

1. 8x2 24. (v – 5)(v – 2) 7. x = -5 only

2. x 25. (p – 3)(p +6) 8. x = 5/3, 4

3. 4 26. 6(v + 10)(v + 1) 9. y = 5, -1

4. 2xy 10. y = 2/3, -1/4

5. z(z - 1) 6.3 11. x = 9, -2

6. 8x2(x2 – 3)

7. 4(2x2 – x – 5) 1. (3x – 2)(x – 1)

8. x2(6x2 – 10x – 3) 2. (2x + 1)(3x + 1)

9. 4(2y3 – 5y2 + 3y – 4) 3. (5x + 9)(x – 2)

10. x2y2(x3y3 +x2y + xy – 1) 4. (2x + 5)(x – 1)

5. (4x + 1)(x + 1)

6.2 6. Not factorable

7. (2x + 5)(x – 1)

1. (b + 7)(b + 1) 8. (2x + 1)(3x – 2)

2. (n – 10)(n – 1)

3. (m – 9)(m + 10) 6.4

4. (n – 2)(n + 6)

5. (n – 1)(n – 9) 1. (x + 2)2

6. (b + 8)2 2. (x + 10)2

7. (m + 6)(m – 4) 3. 2(x – 10)2

8. Not factorable 4. (x – 8)2

9. (k – 5)(k – 8) 5. (p + 4)(p – 4)

10. (a + 2)(a +9) 6. (2x – 5y)(2x + 5y)

11. (n + 7)(n – 8) 7. (4a – 3)(4a + 3)

12. (n – 2)(n – 3) 8. 6(2x – 3)(2x + 3)

13. (b – 4)(b – 2) 9. (y2+1)(y – 1)(y + 1)

14. (n + 2)(n +4) 10. 5(x – 9)(x + 9)

15. 2(n+ 9)(n – 6)

16. 5(n2 + 2n +4) 6.5

17. 2(k + 5)(k + 6)

18. (a – 10)(a + 9) 1. x = 9, 7

19. (p + 10)(p + 1) 2. x = 2, -5/3

20. 5(v – 2)(v – 4) 3. x = 0, 10

21. 2(p – 1 )(p + 2) 4. x = -9, 2

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ANSWERS CHAPTER 7

7.1

1. D

2. C

3. B

4. A

5. D

6. C

7. B

8. A

9. A

10. B

7.2

1. A

2. A

3. D

4. C

5. C

6. D

7. D

8. A

9. A

10. D

7.3

1.7

12x

2. 5

3. m – 2

4. D

5. A

6. C

7. B

8. A

9. B

10. A

11. D

12. D

13. B

14. C

15. B

7.4

1. C

2. C

3. B

4. D

5. C

7.5

1.45

2

2.2

7

3. -8

4. 2

5. -54

6. 31

7. 4

8.37

4

9. -7, 13

10.29

19

11. 2, 4

7.6

1. D

2. D

3. B

4. D

5. C

6. D

72

ANSWERS CHAPTER 8&9

8.1

1. D

2. A

3. D

4. B

5. D

6. C

7. D

8. C

9. B

10. D

11. C

12. C

13. C

14. A

15. C

16. D

17. D

18. B

19. B

20. A

8.2

1. D

2. A

3. C

4. D

5. B

6. A

7. B

8. D

9. C

10. C

8.3

1. B

2. B

3. A

4. B

5. C

6. B

7. D

8. A

9. C

10. D

11. C

12. C

13. B

14. D

15. B

8.4

1. B

2. B

3. D

4. C

5. B

6. D

7. C

8. C

9. A

10. C

11. C

12. D

13. D

9.1&9.3

1. A

2. A

3. C

4. B

5. B

6. B

7. A

8. D

9. D

10. B

11. A

12. C

13. B

14. D

15. D

16. B

9.4

1. C

2. C

3. B

4. D

5. C

6. down, (0, -2)

7. up (0, 5)

8. down (0,-2)

9. up (0, 0)

10. down (0, 0)

11. (0, 0),(5, 0)

12. (-11, 0),(5, 0)

13. (-5 ± 15

5, 0)

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ALGEBRA 2 - cs.stcc.eduHomework List 097/099 Introductory Algebra through Applications Workbook You will find the problems under Additional Exercises Chapter 6 6.1 p. 175 – 176 #