chapter 3 classroom

3.1

1

Simplify the following expressions.

a.

b.

3.1-12

4 7 3h h h

4 3 2 8(5 )(6 )a b a b

Simplify the following expressions.

a.

b.

3.1-23

4 8

3 2

m n

m n

6 5

3

24

9

x y

xy

Simplify the following expressions.

a. c.

b.

3.1-34

3 2 5 4( )x y z

2 5 2(6 )g h

34 6

2

3

5

a b

c

Simplify the following expressions.

a. c.

b.

3.1-45

4 7 3 3 2(2 ) (5 )m n mn

24 6

4

12

4

g h

gh

2 32 5 3

3 2

6 2x z xy

xzxy z

3.2

6

Combine the following functions using addition or subtraction to write a new function that will give the result requested. Represent the new function using function notation.

= The total number of patients treated in the emergency room at a local hospital during the mth month of the year.

= The number of patients in the emergency room treated for heart attack symptoms during the mth month of the year.

The number of patients treated in the emergency room for other problems besides heart attacks during the mth month of the year.

3.2-67

( )P m

( )H m

Combine the following functions.

a.

b.

3.2-78

( ) 3 8 ( ) 4 10f x x g x x

( ) ( )f x g x

( ) ( )f x g x

Combine the following functions.

a.

b.

3.2-109

( ) 3 8 ( ) 4 10f x x g x x

( ) ( )f x g x

( )

( )

f x

g x

Perform the indicated operations and simplify.

a.

b.

3.2-1110

3 2 2 3 2(3 5 4) (4 2 6)m n m n m n mn

3 2 2(8 7 6 ) (3 4 7)x x x x x

Perform the indicated operations and simplify.

c.

d.

3.2-1111

(3 7)(4 5)a a

2(5 2)( 4 4)m m m

3.3

12

H(p) = The hours of overtime needed when a prison is over populated by p prisoners.P(t) = The number of prisoners a prison is over populated by during year t.

Find a function for the number of hours of overtime needed at a prison in year t.

3.3-113

The total cost, C(n), in millions of dollars to educate students at a community college can be modeled by the function

when n hundred students attend.

The number of students in hundreds, S(t), attending the college tyears since 2000 can be modeled by the function

a. Find a function that will calculate the total cost to educate students at this college t years since 2000.

3.3-214

( ) 0.5 1.4C n n

( ) 3 10.2S t t

b. Find the total cost to educate the students at this college in 2012.

3.3-215

( ( )) 1.5 6.5C S t t

c. When was the total cost to educate students at this college $20 million?

3.3-216

( ( )) 1.5 6.5C S t t

Combine the following functions

a.

b.

3.3-317

2( ) 5 8 ( ) 2 6 ( ) 5 2 7f x x g x x h x x x

( ( ))f g x

( ( ))h g x

3.4

18

Factor out the greatest common factor.

a. c.

b. d.

3.4-119

26 10a a

3 2 28 7x y x y

210 4 2m m

3 ( 4) 5( 4)y y y

Factor by grouping.

a.

b.

3.4-220

26 10 15 25p p p

28 12 10 15m mn m n

Factor the following.

a. c.

b.

3.4-321

2 9 14x x

215 23 28x x

2 26 11 3x xy y

Factor the following.

a. b.

3.4-422

263 102 24x x 22 11 40x y xy y

Factor the following.

a. b.

3.4-523

24 7 3x x 3 212 87 21x x x

Factor the following using trial and error.

a. c.

b.

3.4-624

2 7 10x x

2 4 21x x

212 43 35x x

Factor the following using trial and error.

a. c.

b.

3.4-725

2 100x

2 3 24m m

220 30 15x x

3.5

26

Perfect Trinomial Square(positive signs)

(a + b)(a + b)

a2

+ 2ab + b2

Double the product of

1 and last terms

“unsquared” Last term – Perfect

Square

Perfect Trinomial Square(negative middle term)

(a - b)(a - b)

a2

- 2ab + b2

Last term – Perfect

Square

Negative 2 times the

product of 1 and last terms

“unsquared”

= 4x2

+ 12x + 9

Use the pattern to solve.

Ex:1

(2x + 3)2

4x2

+ 12x + 9

2x + 3

Check: Multiply

1st term times 2nd

term times 2.

Same Sign

Factor the following.

a. c.

b.

3.5-130

2 12 36x x

236 60 25a a

2 216 56 49m mn n

Factors of 1st

term

Factors of Last term

a2 – b2 = (a + b)(a – b)

OPPOSITE SIGNS

Factors of 1st

term

Factors of Last term

a 5 5=a2 25–

OPPOSITE SIGNS

+ –a( )( )

Factor the following.

a.

b.

3.5-233

2 64x

2 225 4a b