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1
Simplify the following expressions.
a.
b.
3.1-1
4 7 3h h h
4 3 2 8(5 )(6 )a b a b
2
Simplify the following expressions.
a.
b.
3.1-2
4 8
3 2
m n
m n
6 5
3
24
9
x y
xy
3
Simplify the following expressions.
a. c.
b.
3.1-3
3 2 5 4( )x y z
2 5 2(6 )g h
34 6
2
3
5
a b
c
4
Simplify the following expressions.
a. c.
b.
3.1-4
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
5
Simplify the following expressions. Write all answers without negative exponents.
a. c.
b.
3.1-5
2 3a b
5 2
4 8
3m n
m n
2 3 5
4 4 2
40
6
x y z
x y z
6
Simplify the following expressions. Write all answers without negative exponents.
a. c.
b.
3.1-6
43 8 0(285 )x y z
2 4 2 1 2(5 ) (3 )g h g h
32 2
5 4
30
12
j k
j k
7
Rewrite the following exponents in radical form.
a.
b.
3.1-7
1
4a
3
5p
8
Rewrite the following radicals using rational exponents.
a.
b.
3.1-8
6x
7 2h
9
Simplify the following expressions. Write all answers without negative exponents.
a. c.
b.
3.1-9
1
2 8 281m n
21 2 1 1
3 3 3 310 4x y x y
15 10 1 4
2 3
32
2
x y z
xy z
10
Determine the number of terms in the following polynomial expressions. List the terms as either constant terms or variable terms. Give the coefficient of each variable term.
a.
b.
3.2-1
25 10 20x x
3 54 200a b
11
Determine if the given expression is a polynomial. If the expression is not a polynomial explain why not.
a.
b.
c.
3.2-2
8 7 4a a
2 5 48 9m n mn
25 7g
h
12
For the given expressions, list the degree of each term and the entire polynomial.
a.
b.
3.2-3
25 6 8t t
4 3 2 2 55 7 8a b a b b
13
The revenue and cost for Build It Right Construction to build homes in a new development can be modeled by the following functions.
where R(h) is the revenue in millions of dollars from selling h homes and C(h) is the cost in millions of dollars to build h homes.
a. Find the revenue and cost for Build It Right Construction to build 12 homes in this new development.
3.2-4
2
2
( ) 0.007 0.37 1.04
( ) 0.005 0.23 0.68
R h h h
C h h h
14
The revenue and cost for Build It Right Construction to build homes in a new development can be modeled by the following functions.
where R(h) is the revenue in millions of dollars from selling h homes and C(h) is the cost in millions of dollars to build h homes.
b. Find a new function that will give the profit in millions of dollars for Build It Right Construction when they build h houses in this new development.
3.2-4
2
2
( ) 0.007 0.37 1.04
( ) 0.005 0.23 0.68
R h h h
C h h h
15
c. Use the new profit function to find the profit for 25 houses.
3.2-4
2( ) 0.002 0.14 0.36P h h h
16
The area of a Norman window can be determined by adding the area functions of the rectangle and semicircle pieces that it is made of. If the rectangle part has a height of 80 inches, find the following.
a. A function for the total area of the Norman window as a function of the width of the window.
b. The area of the Norman window if its width is 40 inches.
3.2-5
17
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.
3.2-6
( )P m
( )H m
18
Combine the following functions.
a.
b.
3.2-7
( ) 3 8 ( ) 4 10f x x g x x ( ) ( )f x g x
( ) ( )f x g x
19
Combine the following functions using addition, subtraction, multiplication or division to write a new function that will give the result requested. Represent the new function using function notation.C(w) = the number of cars traded in during week w of the cash for clunkers program.A(w) = the average rebate in dollars earned per car during week w of the cash for clunkers program.P(w) = the total amount paid in dollars for new cars during week w of the cash for clunkers program.N(w) = the number of new cars sold during week w of the cash for clunkers program.
a. The average price paid for a new car during week w of the cash for clunkers program.
3.2-8
20
Combine the following functions using addition, subtraction, multiplication or division to write a new function that will give the result requested. Represent the new function using function notation.C(w) = the number of cars traded in during week w of the cash for clunkers program.A(w) = the average rebate in dollars earned per car during week w of the cash for clunkers program.P(w) = the total amount paid in dollars for new cars during week w of the cash for clunkers program.N(w) = the number of new cars sold during week w of the cash for clunkers program.
b. The total amount of rebates earned in dollars during week w of the cash for clunkers program.
3.2-8
21
The willingness of small appliance manufacturers to produce coffee grinders depends on the price they can sell the coffee grinders for. This situation can be modeled by
Where S(p) represents the supply of coffee grinders in hundreds when p is the price in dollars and the price is greater than $40.
a. Find the number of coffee grinders the manufacturers are willing to supply when the price is $60.
3.2-9
2( ) 0.012 0.6 40S p p p
22
The willingness of small appliance manufacturers to produce coffee grinders depends on the price they can sell the coffee grinders for. This situation can be modeled by
Where S(p) represents the supply of coffee grinders in hundreds when p is the price in dollars and the price is greater than $40.
b. Find a function for the projected revenue if all the coffee grinders that are supplied sell at price p.
3.2-9
2( ) 0.012 0.6 40S p p p
23
The willingness of small appliance manufacturers to produce coffee grinders depends on the price they can sell the coffee grinders for. This situation can be modeled by
Where S(p) represents the supply of coffee grinders in hundreds when p is the price in dollars and the price is greater than $40.
c. Estimate the projected revenue if coffee grinders are sold for $70 each.
3.2-9
2( ) 0.012 0.6 40S p p p
24
Combine the following functions.
a.
b.
3.2-10
( ) 3 8 ( ) 4 10f x x g x x ( ) ( )f x g x
( )
( )
f x
g x
25
Perform the indicated operations and simplify.
a.
b.
3.2-11
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
26
Perform the indicated operations and simplify.
c.
d.
3.2-11
(3 7)(4 5)a a
2(5 2)( 4 4)m m m
27
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.
3.3-1
28
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 t years 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.
3.3-2
( ) 0.5 1.4C n n
( ) 3 10.2S t t
29
b. Find the total cost to educate the students at this college in 2012.
3.3-2
( ( )) 1.5 6.5C S t t
30
c. When was the total cost to educate students at this college $20 million?
3.3-2
( ( )) 1.5 6.5C S t t
31
Combine the following functions
a.
b.
3.3-3
2( ) 5 8 ( ) 2 6 ( ) 5 2 7f x x g x x h x x x
( ( ))f g x
( ( ))h g x
32
The total number of employee days lost at a company to a flu outbreak can be modeled by the function
Where L(E) is the number of lost employee days when E employees catch the flu.The number of employees who catch the flu during a flu outbreak can be modeled by the function
Where E(w) is the number of employees who catch the flu when an outbreak lasts for w weeks.a. Find a function for the number of employee days lost at this company if an outbreak lasts for w weeks.
3.3-4
( ) 2.5 3L E E
( ) 12 3E w w
33
Where is the number of employee days lost at this company when a flu outbreak last w weeks.
b. Use the function you found to determine the number of employee days lost to a 4 week flu outbreak.
3.3-4
( ( )) 30 10.5L E w w ( ( ))L E w
34
Factor out the greatest common factor.
a. c.
b. d.
3.4-1
26 10a a
3 2 28 7x y x y
210 4 2m m
3 ( 4) 5( 4)y y y
35
Factor by grouping.
a.
b.
3.4-2
26 10 15 25p p p
28 12 10 15m mn m n
36
Factor the following.
a. c.
b.
3.4-3
2 9 14x x
215 23 28x x
2 26 11 3x xy y
37
Factor the following.
a. b.
3.4-4
263 102 24x x 22 11 40x y xy y
38
Factor the following.
a. b.
3.4-5
24 7 3x x 3 212 87 21x x x
39
Factor the following using trial and error.
a. c.
b.
3.4-6
2 7 10x x
2 4 21x x
212 43 35x x
40
Factor the following using trial and error.
a. c.
b.
3.4-7
2 100x
2 3 24m m
220 30 15x x
41
Factor the following.
a. c.
b.
3.5-1
2 12 36x x
236 60 25a a
2 216 56 49m mn n
42
Factor the following.
a.
b.
3.5-2
2 64x
2 225 4a b
43
Factor the following.
a.
b.
3.5-3
3 64y
3 327 8m n
44
Factor the following.
a.
b.
3.5-4
4 16m
6 64 256a b
45
Factor.
3.5-5
8 42 3 35x x
