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Houston Community College
Department Of Mathematics
Intermediate Algebra
Review For Exam. III
Review the following problems plus your home work.
1.
Write in lowest term: x2- x- 6
X2 + 5x + 6
2.
Write In lowest term: a3 - 27
a- 3
3.
Find the LCD of the following: y2 – 2y – 8, y2 + 3y + 2
a) x - 3
x+3
b) a2+3a+9
a) (y – 4)(y + 2)(y + 1)
5.
Find numbers that are not in the domain of the following rational
function.
(3 + x) / (x2 – 4x + 3) a) 1 & 3
6.
Add: y
+
y–2
8
2–y
a) ( y – 8) / (y – 2)
Subtract:
-
18
7.
4
X+3
8.
Solve:
2
X-3
x x-3
_
3
x+3
x2 - 9
=
a) - x2 + x - 30
(x+3)(x-3)
12
(x+3)(x-3) a) a) Ø
1
9.
Multiply: x2 + 2x – 15
x2 – 4x + 3
a) x(x – 1)
x–4
10.
Divide: y2 – 4
3y
a) 2y + 4
11.
Subtract:
÷
7x
3x + 1
x2 – x
x2 + x – 20
.
y–2
6y
x–2
3x + 1
-
a)
12.
13.
Simplify: 1 +
x
1 x2
Simplify:
1
y
1
y2
2
a) xy
y-x
x -1
x
+1
–1
a) 1
x+1
14.
Simplify: a3 + b3
a+b
a) a2 + ab + b2
15.
Simplify: y2 – 5y – 14
y2 + y – 2
16.
Simplify: 7 – b
17.
Simplify: 1 - 1
b2 a2
1 - 1
b
a
a) y – 7
y–1
a) – 1
a) a + b
ab
2
18.
Find two positive consecutive integers such that their product is
72.
a) 8 & 9
19.
Factor completely: x4 – 16
20.
Let f(x) = x2 + 3, and g(x) = 2x - 3. Find (f – g)(x)
a) x2 - 2x + 6
21.
Solve: 4x2 - 20x = 0
22.
Solve: - x3 + x2 = - 6x
a) {- 2, 0, 3)
23.
Solve: (x - 1)(x + 1) = 8
a) + 3
24.
The base of a parallelogram is 7 ft more than the height. If the area
of the parallelogram is 60ft2 , what is the measures of the base and
the height? ( Area = bh)
a) (x+2)(x-2)(x2 +4)
a) {0,5}
a) h= 5ft; b = 12ft
x2 + 25 a) Prime
25.
Factor:
26.
Factor: x3 – y3 a) (x – y)(x2 + xy + y2)
27.
Factor:
4x2 – 16x + 12
28.
Factor:
27x3 + 8y3 a) (3x +2y)( 9x2 – 6xy + 4y2)
29.
Factor:
x2 – 8x + 16 a) (x – 4)2
a) 4(x-3)(x-1)
3
30.
Factor:
9x3 + 18x a) 9x(x2 + 2)
31.
Factor:
4x2 – 25 a) (2x-5)(2x+5)
32.
Solve:
(x – 8)(x + 3) = 0
33.
Solve: 3x2 + 7x + 2 = 0 a) { -2, -1/3 }
34.
Factor: 3m4 – 3 a) 3m(x2 + 1)(x + 1)(x-1)
35.
factor: x2 – 36 a) (x-6)(x+ 6)
36.
factor: a3 – 1
a) {- 3,8}
a) (a – 1)(a2 + a + 1)
37.
Solve: 2x2 + 9x -18 = 0 a) {- 6,3/2}
38.
Solve: (2x+1)(x+1) 2(1-x) + 6
{- 7/2,1}
39.
Give the domain of : (x + 6) / (x2 – x – 6) a) – 2, 3 {x|x≠ -2,3}
40.
Reduce: (t2- 9) / (3t + 9) a) (t – 3) /3
41.
Multiply:
42.
Divide:
x2 – 25
. x2 + 7x + 12
X2 + x – 20
x2 - 2x – 15
X2 + x – 20
x2 - 2x – 15 a) (x + 4) /(x – 4)
a3 – b3
a2 – b2

a) (x + 4) /(x – 4)
2a – 2b
2a + 2b
4
a) a2 + ab + b2
a–b
43.
Find the LCM:
44.
Subtract: 4x
y2 – 16, y2- 8y + 16 a) (y – 4)2(y +4)
-
2
X–1
35.
Subtract:
6
r
-
x2 – 1 a) 2(2x – 1) / (x – 1)
x+1
-
4
5
r–3
a) (r – 18) / r(r- 3)
5
GOOD LUCK!!!!!!!
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