EA Exam 3 REVIEW F04
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Nov 24, 2024
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Elementary Algebra
Review for Exam 3
Solve the problem.
1)
After receiving a discount of 15% on its bulk
order of typewriter ribbons, John's Office
Supply pays $5882. What was the price of the
order before the discount? Round to the
nearest dollar if necessary."
Multiply.
2) (-8x
4
)(2x
5
)(-5x
3
)
3) -5x
6
(-8x
5
+ 11x
4
)
4)
(3x + 9)(x + 6)
5)
(3x - 4)(x - 8)
6) (3x
2
+ 3)(4x - 6)
7)
(6p + 7)(6p - 7)
8)
(w - 7)
2
9) (x
2
- 5)
2
10)
(xy + 7)(8xy - 4)
11)
(2x + 7y)
2
12)
(x - 3)(7x
2
+ x + 8)
Evaluate as requested.
13)
Evaluate the polynomial -2x
2
- y
2
+ xy for x =
-2 and y = 5.
Solve the problem.
14)
The polynomial 0.041h - 0.018A - 2.69 can be
used to estimate the lung capacity, in liters, of
a female with height h cm and age A years.
Find the lung capacity of a 20-year-old
woman who is 179 cm tall. Round to the
nearest liter.
Determine the coefficient and the degree of each term in
the polynomial. Then state the degree of the polynomial.
15) a) 8w
5
+ 5w
3
- w
b) -4xyz
5
+ 15x
5
y
4
+ xz
4
Find the total area of all shaded rectangles.
16)
6
x
x
3
Add or subtract, as indicated.
17) a) (x
2
- 8xy + 7y
2
) + (7x
2
- 9xy - y
2
) + (-3x
2
+
xy - y
2
)
b) (3w
4
- 3wz + 9wz
2
) - (6w
4
+ 2wz - 5wz
2
)
Divide.
18) (35x
7
- 49x
4
+ 14x
2
) d
(7x
2
)
19) (x
2
+ 13x + 34) d
(x + 6 )
20) (15x
2
+ 7x - 2) d
(5x - 1)
21)
x
3
+ 125
x + 5
Express using positive exponents. Then, if possible,
simplify.
22) a) 4
- 2
b) 2
3
-3
c) 1
x
-4
d) 4
u
-3
Simplify. Do not use negative exponents in your answer.
23) a) y
-8
œ
y
-4
b) (x
-5
y
-3
)(x
9
y
-7
)
c) 3
-3
œ
3
4
d) (x
9
y
-8
z
-5
)(x
-2
y
-5
z
10
)
Review for Exam 3, page 2
24) a) p
4
p
-5
b) z
-8
z
-4
c) 7x
-6
y
-2
z
3
25) a) (x
-7
)
3
b) (2xy)
-4
c) (x
-2
y
-3
)
-6
d) (2m
4
n
-5
)
3
26) a) x
3
3
-2
b) x
5
y
5
wz
6
-3
c) s
-4
t
-3
6
d) 8x
-3
3y
-5
z
0
Convert to decimal notation.
27) a) 2.84 x 10
7
b ) 8.441 x 10
-5
Convert to scientific notation.
28) a) 33,000,000
b) 0.000080517
Perform the indicated operation. Write the answer in
scientific notation.
29) a) (2.6 ˛
10
-5
)(1.1 ˛
10
-9
)
b) (4.7 ˛
10
-3
)(7.5 ˛
10
7
)
c) 9.12 ˛
10
2
2.4 ˛
10
6
d) 8.04 ˛
10
-8
2 ˛
10
-4
Solve the problem. Express the answer in scientific
notation to two decimals unless requested otherwise.
30)
The earth is approximately 92,900,000 miles
from the sun. If 1 mile = 1.61 x 10
3
m, what is
the distance to the sun in meters?
Provide an appropriate response.
31)
For what values, if any, of x x ≠
0
will x
-3
be
a negative number?
32)
Explain the different meanings of the "-"
symbol for 5 - 2, -3, and 3
-2
.
Factor out the greatest common factor.
33) 4x
12
y
8
- 8x
9
y
7
+ 12x
6
y
5
- 16x
3
y
5
Determine whether the following is a perfect-square
trinomial.
34) a) x
2
+ 18x + 81
b) x
2
- 20x + 400
c) x
2
- 14xy + 49y
2
Factor completely. If the polynomial is prime, state this.
35) x
2
+ 3x - 18
36) x
2
- 8x - 33
37) x
2
- 24 + 2x
38) 3x
4
- 21x
3
+ 30x
2
39) 24x
3
- 62x
2
+ 40x
40) y
2
- 2
3
y + 1
9
41) 15y
2
+ 16y + 4
42) 9z
2
+ 6z - 8
43) 9x
2
- 39xy - 30y
2
44) x
2
- 6x + 36
45)
9 - 30x + 25x
2
46) 25x
2
- 60x + 36
47) 128x
2
- 192x + 72
48) 2x
3
- 4x
2
+ 2x
49) 12x
2
+ 17x + 6
50) y
2
- 36
51) 81p
2
- 4q
2
52) 16x
2
+ 25
53) 4x
2
- 36
54) 49y
4
- 64
55) x
4
- 81
56) 2x
3
- 12x
2
+ 8x - 48
57) 6x
2
- 15x - 8xy + 20y
Review for Exam 3, page 3
Solve the equation.
58)
(x - 7)(x + 6) = 0
59)
11 - 0.8x
5 - 0.2x
= 0
60) x
2
- x = 72
61) 16k
2
- 25 = 0
62) 4x
2
= 5x
63) x
2
+ 3x - 88 = 0
64)
(x + 4)(x - 7) = -10
Find the x-intercepts for the graph of the equation.
65)
y = x
2
- 4x - 12
x
-20 -16 -12
-8
-4
4
8
12
16
y
110
88
66
44
22
-22
-44
-66
-88
-110
x
-20 -16 -12
-8
-4
4
8
12
16
y
110
88
66
44
22
-22
-44
-66
-88
-110
Solve the problem.
66)
The length of a rectangular picture frame is 9
cm more than the width. The area inside the
frame is 90 square cm. Find the dimensions of
the frame.
67)
One leg of a right triangle is 6 cm shorter than
the other leg. The length of the hypotenuse is
30 cm. Find the length of the shorter leg.
68)
A 10-ft ladder is leaning against a building. If
the bottom of the ladder is 6 ft from the base of
the building, how high does the ladder reach?
69)
In a sports league of n teams in which each
team plays every other team twice, the total
number N of games to be played is given by N
= n
2
- n. How many teams are in a softball
league if the total number of games played is
56?
70)
If an object is propelled upward from a height
of 96 feet at an initial velocity of 80 feet per
second, then its height after t seconds is given
by the equation h = -16t
2
+ 80t + 96, where h is
in feet. After how many seconds will the object
reach a height of 196 feet?
Provide an appropriate response.
71)
Explain the difference between a factor and a
multiple of a number.
72)
Explain the error in the following:
x
2
+ 2x - 15 = (x - 5)(x + 3)
73)
What is the difference between a trinomial and
a quadratic equation?
74)
Will there always be two different solutions
when the principle of zero products is used to
solve a quadratic equation? Why or why not?
75)
What is wrong with solving x
2
= 6x by
dividing both sides of the equation by x?
76)
Explain the error in the following:
x
2
- y
2
= (x - y)
2
77)
Explain the error in the following:
25x
2
- 100 = (5x + 10)(5x - 10)
78)
Explain the error in the following:
x
2
+ 16 = (x + 4)(x - 4)
79)
How could you use factoring to convince
someone that x
2
- y
2
≠
(x - y)
2
?
80)
Explain the error in the following, assuming
you were to factor completely:
81x
4
- 1 = (9x
2
+ 1)(9x
2
- 1)
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Answer Key
Testname: EA EXAM 3 REVIEW F04
1) $6940
2) 80x
12
3) 40x
11
- 55x
10
4) 3x
2
+ 27x + 54
5) 3x
2
- 28x + 32
6) 12x
3
- 18x
2
+ 12x - 18
7) 36 p
2
- 49
8) w
2
- 14w + 49
9) x
4
- 10x
2
+ 25
10) 8x
2
y
2
+ 52xy - 28
11) 4x
2
+ 28xy + 49y
2
12) 7x
3
- 20x
2
+ 5x - 24
13) -43
14)
4 liters
15) a) Coefficients: 8, 5, -1;
degrees: 5, 3, 1
degree of polynomial: 8
b) Coefficients: -4, 15, 1
degrees: 7, 9, 5
degree of polynomial: 9
16) x
2
+ 9x + 18
17) a) 5x
2
- 16xy + 5y
2
b) -3w
4
- 5wz + 14wz
2
18) 5x
5
- 7x
2
+ 2
19)
x + 7 - 8
x + 6
20)
3x + 2
21) x
2
- 5x + 25
22) a) 1
16
b) 8
27
c) x
4
d) u
3
64
23) a) 1
y
12
b) x
4
y
10
c) 3 d) x
7
z
5
y
13
24) a) p
9
b) 1
z
4
c) 7y
2
x
6
z
3
25) a) 1
x
21
b) 1
16x
4
y
4
c) x
12
y
18
d) 8m
12
n
12
26) a) 9
x
6
b) w
3
z
18
x
15
y
15
c) t
18
s
24
d) 1
27) a) 28,400,000
b) 0.00008441
28) a) 3.3 ˛
10
7
b) 8.0517 ˛
10
-5
29) a) 2.86 ˛
10
-14
b) 3.525 ˛
10
5
c) 3.8 ˛
10
-4 d) 4.02 ˛
10
-4
30)
1.50 x 10
11
m
31)
If x is negative, the answer will be negative.
32)
Subtraction; negative, or opposite; reciprocal
33) 4x
3
y
5
(x
9
y
3
- 2x
6
y
2
+ 3x
3
- 4)
34) a) Yes
b) No
c) Yes
35)
(x + 6)(x - 3)
36)
(x + 3)(x - 11)
37)
(x + 6)(x - 4)
38) 3x
2
(x - 5)(x - 2)
39)
2x(4x - 5)(3x - 4)
40)
y - 1
3
2
41)
(3y + 2)(5y + 2)
42)
(3z - 2)(3z + 4)
43)
3(3x + 2y)(x - 5y)
44) Prime
45)
(5x - 3)
2
46)
(5x - 6)
2
47)
8(4x - 3)
2
48)
2x (x - 1)
2
49)
(4x + 3)(3x + 2)
50)
(y + 6)(y - 6)
51)
(9p + 2q)(9p - 2q)
52) Prime
53) 4 x+3
x-3
54) (7y
2
+ 8)(7y
2
- 8)
55) (x
2
+ 9)(x - 3)(x + 3)
56)
2(x - 6)(x
2
+ 4)
57)
(2x - 5)(3x - 4y)
58)
7, -6
59)
13.75, 25
60)
-8, 9
61)
5
4
, - 5
4
62)
5
4
, 0
63)
-11, 8
64)
-3, 6
Answer Key
Testname: EA EXAM 3 REVIEW F04
65)
(-2, 0), (6, 0)
66)
width = 6 cm, length = 15cm
67)
18 cm
68)
8 ft
69) 8
70)
2.5 sec
71)
A factor is a number in a product while a multiple of
a number is a product of it and some natural number.
For example, 6 = 2 œ
3, so 2 and 3 are FACTORS of 6;
18 = 3 x 6, so 18 is a MULTIPLE of 6.
72)
The factorization yields a middle term of -2x rather
than 2x:
x
2
+ 2x - 15 = (x + 5)(x - 3)
73)
A trinomial is the sum of three monomials. It is not an
equation. A quadratic equation is an equation of the
form ax
2
+ bx + c = 0, a ≠
0.
74)
No; whenever ax
2
+ bx + c is a trinomial square, then
x
2
+ bx + c has only one solution.
75)
One solution of the equation is 0. Dividing both sides
of the equation by x, leaving the solution x = 6, is
equivalent to dividing by 0.
76) x
2
- y
2
is a difference of squares, not a binomial
square.
x
2
- y
2
= (x + y)(x - y)
77)
The largest factor has not been factored out:
25x
2
- 100 = 25(x + 2)(x - 2)
78)
The polynomial x
2
+ 16 is not a difference of squares.
Since x
2
+ 16 is a sum of squares with no common
factor, it cannot be factored.
79) x
2
- y
2
= (x + y)(x - y) ≠
(x - y)
2
80)
The polynomial is not factored completely since 9x
2
-
1 can be factored further:
81x
4
- 1 = (9x
2
+ 1)(3x + 1)(3x - 1)