College algebra

Page 369-370 21-48 multiples of 3 and 51-72 multiples of 3

Page 379-380 5,9,13,17 and 36-60 multiples of 4

Page 306 35-50 multiples of 5

Page 385 5-25 multiples of 5

Page 395 12-22 even and 39

Plus exam

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X Intermediate Alg Exam 4…
Date
Intermediate Algebra
Exam 4
Name
Determine the value or values of the variable where the expression is defined.
X – 7
1)
x² – 9
Simplify the rational expression.
y3 – 27
2)
y – 3
Add or subtract.
m2 – 11m
3)
30
+
m – 5
m – 5
4)
6 8
+
х X-2
1
5)
X + 2
2x + 3
x2 – 2x – 3 x2 + 8x + 7
a
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X Intermediate Alg Exam 4…
5)
X + 2
2x + 3
x2 – 2x – 3×2 + 8x + 7
Multiply
6)
x2 + 14x + 45
x² +66
x2 + 15x + 54 x2 – 4x – 45
Divide.
7)
3×2 x3
5 30
.
8)
x2 + 11x + 30
x2 + 12x + 35
x² + 6x
x2 + 15x + 56
Simplify the rational expression.
y2 + 4y – 32
9)
y2 + 3y – 40
2
x2 + 5x + 6
a
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X Intermediate Alg Exam 4…
2
10)
x2 + 5x + 6
x2 + 7x + 10
Simplify
4 +
2
х
11)
х
4
+
1
8
Divide using long division.
8m3 + 12m2 – 4m + 8
12)
m + 2
3
a
Open With
© Print
7. The rational expression
x – 2x – 15
x + 3x – 40
Section 6.1 The Domains of Rational Functions and Multiplication and Division of Rational Expressions
369
simplifies to
*
x?
9. The quotient
8. The product
yo
.
y
y
10. The
domain
of
the
function f(x)
* + 5
=
* – 4
is
Practice the Skills
Determine the values that are excluded in the following expressions.
e out
7
11.
12.
x + 2
he
x² – 64
. – 3
16.
Try Exercise 59
15 + 12
-2
49 – r?
4
13.
2.×2 – 15x + 25
x2 + 81
17.
x? – 81
2
14.
(x – 6)2
x² – 36
18.
x + 36
Determine the domain of each function.
19. f(x)
X – 4
X-5
20. f(z) =
9
21. y =
22. yx2 + 4x – 21
23. f(a)
3
-18z + 9
a? + 3a + 2
a? + 4a + 3
x² – 64x
x2 + 81
5
x² + x – 6
10 – 3x
24. f(x)
x² + 8x
a + 36
27. m(a)
a² – 36
r –
x² – x + 8
x² + 4
b2 – 36
6² + 36
y by the
25. 8(x)
26. h(x)
cal of the divisor.
28. k(b)
Simplify each rational expression.
x2 + x
x² – 5x
Further; divide
mon factors.
29.
30.
31.
5×2 – 20xy
15.x
X
– X
32.
4x²y + 12xy + 18.rºy3
34.
10.xy?
p- 2p – 24
37.
ry Exercise 6
6 – P
y? – 10yz + 24z?
40.
y? – 5yz + 4z?
(x + 6)(x – 3) + (x + 6)(x – 2)
43.
2(x + 6)
ry – yw + xz ZW
46.
xy + yw + xz + zw
–
that you under-
r? + 7x
x
33.
x² – 2x
x² – 1
Sr – 8
4×2 – 16x + 6xy
35.
36.
8 – 5r
14x®y?
4×2 – 9
a- 3a – 10
38.
39.
2x² – x – 3
a² + Sa+ 6
8x? – 125y
64×3 – 2773
41.
42.
2x – 5y
32 – 4x
(2x – 1)(x + 4) + (2x – 1)(x + 1) a+ 7a – ab – 7b
45.
44.
3(2x – 1)
a? – ab + 5a – 56
x² – x – 12
a² – 6²
48.
47.
a? – b
x3 + 27
Multiply or divide as indicated. Simplify all answers.
3.x y
49.
5y9
3
51.
4. 16y?
3-rr – 9
53.
1-39-
x2 + 3x – 10
x² – 3x
55.
x² – 5x + 6
r2 + 10 + 21
57.
rt 7
x + 12x + 35
59.
x² + 4x – 5
.
9×3
32×2 5.r
50.
y 8y?
10m” 25m
52. 49.x?y? 21x” y
7a + 75 a² – 6²
54.
5
p + 7p + 10 1
56.
{x/x = -5/
a – b
P + 5
P + 2
r + 3x – 18
first factor the
le out any com-
58. (1-3) –
4x
.
(r2 – 57 – 24)
. +1
73
60.
7s, first factor all
ut the common
8x + 8
x – 17x + 30 x + 78 – 18
2r? + 8xy + 8y? 2r? + 7xy + 6yº
62.2 + 4xy + 4y4r? + 14ry + 127
r2 + 3x – 28
7x – 7
a² – ²
ssions, multiply
al of the second
a-b
61.
9a + 9b
a² + 2a + 1
370
Chapter 6 Rational Expressions and Equations
65.
3x – x – 4 2x? – 5x – 12
41² + 5x + 1 6x² + 8 – 12
x + 2(x – 2)
62
2x + x
x² – 1
x – 2×2 + x
66.
ys
68.
x?
+ y?
y
a?
Simp
97.
8a
For
Xy – 2y
(x + y)
67,
2xy + y²
2x + 4r x + 2
6x + 14x + 4 3x + x
(a – b) a – b
71.
b! (a – b)
4x + y 10r?
73.
5x + 2y 8x²
2xy
ad + bc) bd pc + pd – qc
75.
ac + ad + bc + bd pc pd + qe
3r? + 1778 + 10s?
6r? + rs
77.
6r2 + 13rs
6r
y?
00
99
qd
qd
1
2a + 1
70.
4a² + 2a + 1 (a – 1)
16
m2 + 8 + 16
72.
64 r2 + 4r + 16
2x² – 7x² + 3x x² + 3x
74.
x² + 2x – 3 (x – 3)²
2p2 + 2pq
pq? – q?
76.
p² + p + p q + 9
ptp² + pq² + q² p² + P + p + 1
x3
4x² + x – 4 2x² + 2x² + x + 1
78.
x5
x + x² – x² 2x² – 8x² + x – 4
103
55?
252
Srs +32
X
y
y – 20
x – 3
y + 4
y + 1
Problem Solving
Determine the polynomial to be placed in the shaded area to give a true statement.
1
79.
80.
x? + 2x – 15
3x + 2
y?
81.
82.
6p2 + p – 15
– 3
С.
=
2p – 1
2p – 3
10
10
x – 2
10
.
=
area
Determine the polynomial to be placed in the shaded area to give a true statement.
r 7 – 12
83.
x² – 4 2x² + x – 6
= 1
84.
x² + 2x – 3 x² – 2x – 8
(x + 2)
2x+5
x² – 9 2×2 – 9x + 9 x + 3
472 – r
85.
18 4r3 – 9r2
3r – 1)
2.×2 + 3x – 2
86.
2x – 1
6r2 – 9r + 3 r2
87. Area Consider the rectangle below. Its
is 88. Area Consider the rectangle below.
3a? + Tab + 262 and its length is 2a + 4b. Find its width, w,
in terms of a and b, by dividing its area by its length.
terms of a and b, by dividing its area by its length.
1
Its
area is
1
W
a2 + 2ab + b2 and its length is 3a + 3b. Find its width, w, in
2a + 4b
W
3a + 3b
area
89. Area Consider the triangle below. If its
is
a² + 4ab + 3b2 and its base is a + 3b, find its height h. Use
1
area = (base) (height).
2
90. Area Consider the trapezoid below. If its area is
1
a² + 2ab + b², find its height, h. Use area =
2
z hla+b).
b
a + 3b
a
Challenge Problems
Perform each indicated operation.
2.×2 – 3x – 14 6×2 + x – 15 6×2 – 7x – 3
91.
2x² – 9x + 7 7 3x² + 2x – 5 2x – x – 3
5x²(x – 1) – 3x(x – 1) – 2(x – 1) 2x + 1
93.
10x?(x – 1) + 9x(x – 1) + 2(x – 1) x + 3
(x – p)” (x – p)2n
95.
92.
94.
x?(3x – y)
x2
x 6
a? – b 2a? – 7ab + 3b ab – 3b
2a² – 3ab + b a² + ab
a + 2ab + b
-y)- 5x(3x – y) – 24(3x – y) x-1
x+(3x – y) – 9x(3x – y) + 8(3x – y) ++ 3
96.
25
(a – b)
(a – b) +2