Mth 100 Sec 7.1 - 8.5
Practice exam #3. These are additional problems to those on the homework, quizzes and class notes. In addition 20% of the
material will be from previous test and thus the prior material must be reviewesd and studied._
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the greatest common factor of the terms.
1) 18ab, -10a 2 , 10ab2 , -6b2
2) 21m 3 , 189m 7 , 441m 4
3) 5d6 (f + g)3 , 13d4 (f + g)2
Factor out the greatest common factor.
4) 15wx - 20wy - 25wz
5) 7x5 y6 - 4r5 s 6 - m 5 p6
6) t(9 - m) + s(9 - m)
Factor by grouping.
7) x3 + 7x2 - 8x - 56
8) 20wx - 5wy - 4xz + yz
9) ya 2 + yb2 - 7a 2 - 7b2
Factor the trinomial completely.
10) y2 + 5y - 14
11) x2 + 6xy - 135y2
12) z 2 - 2zw + 63w2
13) -25x2 + 30x + 16
14) 20a 2 + 3ab - 9b2
15) 40m 2 + 41mn + 10n 2
16) -54k2 - 45k + 54
17) 4x3 + 8x2 - 32x
1
Factor the polynomial completely.
18) (r + s)2 + 18(r + s) + 81
Factor the trinomial completely.
19) 12(p + 1)2 + 13(p + 1) + 3
Factor the polynomial completely.
20) 144k2 - 25m 2
21) z 3 - 27p3
22) 125a 3 - 8b3
Factor the polynomial.
23) 14t3 + 2t2 - 16t
Factor the polynomial completely.
24) 8c4 - 18d4
Factor the polynomial.
25) 245a 2 - 80b2
Factor the polynomial completely.
26) 12a 2 - 27b2
Find all solutions by factoring.
27) 25x2 + 40x = -16
28) 25x2 - 4 = 0
29) 4x2 + 20x = -25
Find all numbers that are not in the domain of the function. Then give the domain using set notation.
6
30) f(x) = x2 + 11x + 28
31) f(x) = x2 + x - 6
7x2 - 13x - 2
Express the rational expression in lowest terms.
40m 2 p2
32)
8m 8 p
2
33)
z 3 + 8
3
z - 2z 2 + 4z
34)
3x - 3y - bx + by
3x - 3y + bx - by
35)
9x2 - 25y2
6x2 - 31xy + 35y2
Perform the indicated operation and express in lowest terms.
4p2
2p - 2
· 36)
p
7p - 7
37)
k2 + 13k + 36
k2 + 8k
· k2 + 17k + 72 k2 - 3k - 28
38)
5p - 5 9p - 9
÷ p
2p2
39)
2x2 - 9x + 9 3x2 + 11x - 4
· 3 - x
2x2 + 5x - 12
40)
3
3
+ 2
8x
8x2
41)
m 2 - 9m
18
+ m - 3
m - 3
42)
43)
44)
45)
8x3
4x2 + 10xy + 25y2
- 125y3
4x2 + 10xy + 25y2
9
9
+ r r - 6
x
x2 - 16
- 7
x2 + 5x + 4
12
7
+ x
6x
3
Simplify the complex fraction.
x
3
46)
7
x + 4
9 + 47)
1
x
+ 4 12
1 - 5
x
1 + 5
x
48)
49)
50)
3
x
64p2 - 25q2
pq
8 5
- q p
7 + y
y
+ y
7 - y
y
7 - y
+ 7 + y
y
51)
x-2
x-2 - y-2
52)
m -1 + z -1
m -1 - z -1
Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as
potential solutions. Then give the domain using set notation.
2
10
53)
- = 0
x - 12 x + 16
Solve the equation.
t
2
54) = t
-3t - 4
55)
6
8
= 1 + x - 6
x + 6
4
56)
2y + 3 3
= y
2
57)
4x - 5 2x -1
= 2x + 1
x + 5
Solve the problem.
1 1 1
58) A formula for electric circuits is = + . If a = 15 and b = 19, find c.
a b c
1 1 1
59) A formula for electric circuits is = + . If c = 19 and b = 8, find a.
a b c
60) A gas law in chemistry says that PV pv
= . If T = 310, t = 400, V = 11, P = 40, and v = 9, find the value of p.
T
t
Round to the nearest thousandth.
Solve the formula for the specified variable.
9
61) F = C + 32 for C
5
62) P = A
for r
1 + rt
63) A = P(1 + nr) for r
1
64) V = Bh for h
3
65)
1 1
+ = c for b
a b
5
Answer Key
Testname: 100 PRACTICE PROB TEST 3 7.1 TO 8.5
1) 2
2) 21m 3
3) d4 (f + g)2
4) 5w(3x - 4y - 5z)
5) Cannot be factored
6) (t + s)(9 - m)
7) (x + 7)(x2 - 8)
8) (4x - y)(5w - z)
9) (a 2 + b2 )(y - 7)
10) (y + 7)(y - 2)
11) (x + 15y)(x - 9y)
12) Prime
13) -(5x + 2)(5x - 8)
14) (4a + 3b)(5a - 3b)
15) (8m + 5n)(5m + 2n)
16) -9(3k - 2)(2k + 3)
17) 4x(x - 2)(x + 4)
18) (r + s + 9)2
19) (4p + 7)(3p + 4)
20) (12k + 5m)(12k - 5m)
21) (z - 3p)(z 2 + 3zp + 9p2 )
22) (5a - 2b)(25a 2 + 10ab + 4b2 )
23) 2t(7t2 + t - 8)
24) 2(2c2 + 3d2 )(2c2 - 3d2 )
25) 5(7a + 4b)(7a - 4b)
26) 3(2a + 3b)(2a - 3b)
4
27) - 5
28)
2
2
, - 5
5
29) - 5
2
30) -7, -4; {x|x ≠ -7, -4}
1
1
31) - , 2; x x ≠ - , 2
7
7
32)
5p
m6
33)
z + 2
z
34)
3 - b
3 + b
35)
3x + 5y
2x - 7y
36)
8p
7
6
Answer Key
Testname: 100 PRACTICE PROB TEST 3 7.1 TO 8.5
37)
k
k - 7
38)
10p
9
39) -(3x - 1)
3
40)
4x2
41) m - 6
42) 2x - 5y
18r - 54
43)
r(r - 6)
44)
x2 - 6x + 28
(x - 4)(x + 4)(x + 1)
45)
79
6x
46)
x(x + 4)
21
47)
36
x
48)
x - 5
x + 5
49) 8p + 5q
7 + y
50)
7 - y
51)
y2
2
y - x2
52)
z + m
z - m
53) 12, -16; {x x ≠ 12, -16}
54) {-2, -4}
55) {10, -12}
56) {-6}
8
57) 5
58) 71.250
59) 5.630
60) 63.082
5
61) C = (F - 32)
9
62) r = A - P
Pt
63) r = A - P
Pn
64) h = 3V
B
7
Answer Key
Testname: 100 PRACTICE PROB TEST 3 7.1 TO 8.5
65) b = a
ac - 1
8