Elementary Algebra - Review for Exam 3
Simplify.
1) a) 7 6 · 7 4
b) (6x3)(2x5)
c) g7 · g3 · g8
d) (y + 3)8(y + 3)6
2) a) (pq6)(pq)3
b) (3r7)2
c) (x7y)3(x5y6)
3) a)
a6
a2
c)
m 9p 7
m 4p
e)
22u8v2
2u5v
4) a)
c)
e)
b)
d)
20k3
5k
60x5
-10x3
Add or subtract, as indicated.
8) a) (x2 - 8xy + 7y2)
+ (7x2 - 9xy - y2)
+ (-3x2 + xy - y2)
b)
(3w4 - 3wz + 9wz 2)
- (6w4 + 2wz - 5wz 2)
Multiply.
9) a) (-8x4)(2x5)(-5x3)
b) -5x6(-8x5 + 11x4)
c) (x - 3)(7x2 + x + 8)
10) a) (3x + 9)(x + 6)
b) (5x - 8)(x - 12)
11) a) (6p + 7)(6p - 7)
b) (4x - 1)(4x + 1)
2 3
x
b)
5n 4
2
x5y 4
z2
d)
2x6y4 2
9z 8
5a7 0
2b5c4
Determine the leading term, leading coefficient, and
the degree of the polynomial.
5) a) 3x2 + 4x - 3
b) 3x6 - 7x7 + 8x2 - 8
Evaluate as requested.
6) Evaluate the polynomial
a) y2 - 3y + 9 for y = 4
b) -2x2 - y2 + xy for x = -2 and y = 5.
c) -2x3 - 6x2 - 26 for x = -3
12) a) (w - 7)2
b) (2x + 7y) 2
c) (x2 - 5)2
13) a) (3x2 + 3)(4x - 6)
b) (xy + 7)(8xy - 4)
Divide.
14) a)
b)
-10x10 + 25x6
-5x
c) (35x7 - 49x4 + 14x2) ÷ (7x2)
Express using positive exponents. Then, if possible,
simplify.
2 -3
15) a) 4 - 2
b)
3
c)
Solve the problem.
7) 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.
16x4+ 56x
8
1
x-4
d)
4 -3
u
Simplify. Do not use negative exponents in your
answer.
16) a) y-8· y-4
b) (x-5y-3)(x9y-7)
c) 3 -3 · 3 4
d) (x9y-8z -5)(x-2y-5z10)
Review for Exam 3, Page 2
17) a)
p4
p-5
b)
z-8
z-4
c)
7x-6
y-2z 3
29) x2 - 24 + 2x
30) 3x4 - 21x3 + 30x2
18) a) (x-7)3
c) (x-2y-3)-6
b) (2xy)-4
d) (2m 4n -5)3
31) 24x3 - 62x2 + 40x
19) a)
x3 -2
3
b)
x5y5 -3
wz 6
32) y2 -
c)
s-4 6
t-3
d)
8x-3 0
3y-5z
33) 15y2 + 16y + 4
34) 9z 2 + 6z - 8
Convert to decimal notation.
20) a) 2.84 x 107
b ) 8.441 x 10-5
Convert to scientific notation.
21) a) 33,000,000
b) 0.000080517
Perform the indicated operation. Write the answer in
scientific notation.
22) a) (2.6 × 10-5)(1.1 × 10-9)
b) (4.7 × 10-3)(7.5 × 107)
c)
9.12 × 102
2.4 × 106
2
1
y+
3
9
d)
8.04 × 10-8
2 × 10-4
Solve the problem. Express the answer in scientific
notation to two decimals unless requested otherwise.
23) The earth is approximately 92,900,000
miles from the sun. If 1 mile = 1.61 x 103 m,
what is the distance to the sun in meters?
Factor out the greatest common factor.
24) a) 5x2 - 35x
b) 60m 8 - 60m 5 - 48m 3
c) 4x12 y8- 8x9y7 + 12x6y5 - 16x3y5
Factor completely. If the polynomial is prime, state this.
25) 2x3 - 12x2 + 8x - 48
35) 9x2 - 39xy - 30y2
36) x2 - 6x + 36
37) 12x2 + 17x + 6
38) 25x2 - 60x + 36
39) 9 - 30x + 25x2
40) 128x2- 192x + 72
41) 2x3 - 4x2 + 2x
42) y2 - 36
43) 81p2 - 4q2
44) 16x2 + 25
45) x4 - 81
46) 49y4 - 64
26) 6x2 - 15x - 8xy + 20y
27) x2 + 3x - 18
28) x2 - 8x - 33
Determine whether the following is a perfect-square
trinomial. If so, factor the trinomial.
47) a) x2 + 18x + 81
b) x2 - 20x + 400
c) x2 - 14xy + 49y2
Review for Exam 3, Page 3
Provide an appropriate response.
48) Explain the difference between a factor and
a multiple of a number.
49) Explain the error in the following:
x2 - y2 = (x - y)2
50) Explain the error in the following:
25x2 - 100 = (5x + 10)(5x - 10)
51) Explain the error in the following:
x2 + 16 = (x + 4)(x - 4)
Solve the equation.
52) 66 = 14x + 8x
53)
2
1
x- x=4
5
3
54) 9x - (4x - 1) = 2
55) -4x + 2(-3x - 6) = -15 - 7x
Write the slope-intercept equation for the line with the
indicated slope and y-intercept.
3
56) Slope ; y-intercept (0, 2)
4
Write a point-slope equation for the line with the given
slope that contains the given point.
57) m = -2; (5, -3)
Write the slope-intercept equation for the line
containing the given pair of points.
58) (-2, 3) and (2, 5)
Graph the line.
59) The line with slope
the point (4, 2)
60) y =
1
x+3
5
61) y + 2 = -
1
(x - 3)
4
3
that passes through
2
Find the intercepts, then graph the equation.
62) -2x + 5y = 10
Solve the problem.
63) A tax-exempt school group received a bill
of $270.71 for educational software. The bill
incorrectly included sales tax of 7%. How
much should the school group pay?
64) In a local election, 24,300 people voted. This
was a decrease of 8% over the last election.
How many people voted in the last
election? Round to the nearest whole
person if necessary.
Answer Key
Testname: EAREVIEW3_SPRING2012
b) 12x8
1) a) 7 10
c) g18
d) (y + 3)14
2) a) p4q9
b) 9r14 or 3 2r14
c) x26y9
b) 4k2
3) a) a 4
c)
23
8
or
3
x3
x
x20y4
z8
b)
d)
5 4n 4
625n 4
or
4
16
2
4x12y8
2 2x12y8
or
81z 16
9 2z 16
e) 1
5) 3x2 , 3, 2
6) a) 13
b) -43
c) -26
7) 4.289 liters
8) a) 5x2 - 16xy + 5y2
b) -3w4 - 5wz + 14wz2
9) a) 80x12
b) 40x11 - 55x10
c) 7x3 - 20x2 + 5x - 24
10) a) 3x2 + 27x + 54
b) 5x2 - 68x + 96
11) a) 36 p2 - 49
b) 16x2 - 1
12) a) w2 - 14w + 49
b) 4x2 + 28xy + 49y2
c) x4 - 10x2 + 25
13) a) 12x3 - 18x2 + 12x - 18
b) 8x2y2 + 52xy - 28
14) a) 2x4 + 7x
b) 2x8 - 5x4
c) 5x5 - 7x2 + 2
15) a)
1
16
c) x4
16) a)
1
y12
c) 3
b)
27
8
d)
u3
64
b)
x4
y10
d)
x7z 5
y13
1
z4
1
x21
b)
1
16x4y4
c) x12y18
d)
8m 12
n 12
19) a)
9
x6
b)
w3z18
x15y15
c)
t18
s24
d) 1
18) a)
c) m 5p6 d) -6x2
e) 11u3v
4) a)
b)
17) a) p9
c)
7y2
x 6z 3
20) a) 28,400,000
b) 0.00008441
b) 8.0517 × 10-5
22) a) 2.86 × 10-14
b) 3.525 × 105
d) 4.02 × 10-4
c) 3.8 × 10-4
11
23) 1.50 x 10 m
24) a) 5x(x - 7)
b) 12m 3(5m 5 - 5m 2 - 4)
c) 4x3y5(x9y3 - 2x6y2 + 3x3 - 4)
25) 2(x - 6)(x2 + 4)
26) (2x - 5)(3x - 4y)
27) (x + 6)(x - 3)
28) (x + 3)(x - 11)
29) (x + 6)(x - 4)
30) 3x2(x - 5)(x - 2)
31) 2x(4x - 5)(3x - 4)
1 2
32) y 3
21) a) 3.3 × 107
33) (3y + 2)(5y + 2)
34) (3z - 2)(3z + 4)
35) 3(3x + 2y)(x - 5y)
36) Prime
37) (4x + 3)(3x + 2)
38) (5x - 6)2
39) (3 - 5x)2 or (5x - 3)2
40) 8(4x - 3)2
41) 2x (x - 1)2
42) (y + 6)(y - 6)
43) (9p + 2q)(9p - 2q)
44) Prime
45) (x2 + 9)(x - 3)(x + 3)
46) (7y2 + 8)(7y2 - 8)
47) a) Yes: (x + 9)2 b) No c) Yes: (x - 7)2
48) 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 · 3, so 2 and 3 are
FACTORS of 6; 18 = 3 x 6, so 18 is a MULTIPLE of
6.
Answer Key
Testname: EAREVIEW3_SPRING2012
49) x2 - y2 is a difference of squares, not the square of a
binomial.
x2 - y2 = (x + y)(x - y)
50) The largest factor has not been factored out:
25x2 - 100 = 25(x + 2)(x - 2)
51) The polynomial x2 + 16 is not a difference of
squares. Since x2 + 16 is a sum of squares with no
common factor, it cannot be factored.
52) 3
53) 60
1
54)
5
55) 1
56) y =
3
x+2
4
57) y + 3 = -2(x - 5)
1
58) y = x + 4
2
y
10
5
-10
-5
5
10 x
5
10 x
5
10 x
-5
-10
59)
y
10
5
-10
-5
-5
-10
60)
y
10
5
-10
-5
-5
-10
61)
62) (-5, 0), (0, 2)
63) $253.00
64) 26,413 people