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Assignment #1 MAT121 Summer 2014
NAME:_______________________
Directions: Do ALL of your work on THIS handout in the space provided! Circle your final answer!
On problems that your teacher would show work on be sure that you also show work on!
This assignment is DUE on or before 8:00 a.m. Monday May 19th (see your syllabus for late penalty!).
1.1 Greatest Common Factor
1. Factor out the GCF. 14x3 – 7x2 + 7x
2. Factor out a (-1) from the polynomial.
3–x
Factor each polynomial by factoring out the opposite of the GCF.
3. -4x3 + 12x2
4. -12x3 + 4x2 – 8x
5. 6 – 3z
1.2 Factoring Trinomials of the Form x2 + bx + c
Factor each trinomial, state if a polynomial is prime.
6. y2 – 10y +16
7. x2 + x – 20
8. c2 + 12c + 20
9.
10. x2 + x + 3
Factor each trinomial. Make sure to factor out a negative and/or the GCF where applicable.
11. 3x2 +12x –36
12. -2x3 – 10x2 + 12x
13. -x2 – 7x –10
1.3 Factoring Trinomials in the Form ax2 + bx + c where a
1
Factor, (if a polynomial is prime, say so)
14. 3x2 + 10x + 7
15. 2b2 – 15b + 7
16. 6y2 – 7y – 5
Factor. Make sure to factor out a negative and/or the GCF where applicable.
17. 20x3 – 18x2 + 4x
18. -16x2 + 44x – 10
1.4 Factoring Binomials
Completely factor the binomials, remember to factor out the GCF first when applicable (if a problem is prime say so).
19. 25a2 – 81
20. x3 – 64x
21. x4 – 16
22. x2 + 4
23. b3 + 27
24. x3 – 64
25. 16x3 + 54
1.5 Solving Quadratic Equations by Factoring
Solve each equation.
26. (2x – 1)(3x+4) = 0
27. x(x – 1)(x+2) = 0
28. x2 – 14x + 45 = 0
29. 25x2 – 16 = 0
30. 4x2 + 2x – 6 = 0
31. 5x2 – 20 = 0
32. (x – 2)(x – 3)= 6
33. x(x – 3) +2 = 30
34. 2x(x – 3) = 5x(x– 4) +8
2.1 Introduction to Rational Expressions
Substitute the given number into the expression and simplify (if possible).
35.
x 3
let x  3
x  4x 1
36.
 a  1 a  2 
 a  3 a  4 
2
let a  3
Write the domain of the expression using words and in interval notation.
37.
38.
y4
y  5y  6
2
x 1
x2
Reduce the expression to lowest terms.
39.
40.
20 xy 3
16 x5 y
10  m  3
12  m  3 m  1
41.
10 x  20
x2  4
42.
2 y2  y  6
y2  y  2
43.
3x  6
12  6 x
2.2 Multiplication and Division of Rational Expressions
Multiply or divide as indicated.
44.
3 30

10 5
45.
3x  21 3x 2

6x
4 x  28
46.
4a  16 a  4

3a  15 2a  10
47.
p 2  2 p  1 16 p 2  1
 2
4 p 1
p 1
48.
2 x 2  5 x  12 2 x 2  3x  9

3x 2  8 x  16 3x 2  13x  12
2.3 Least Common Denominator
Fill in the blank to convert the expressions to equivalent expressions with the indicated denominator.
49.
2

11 33
50.
x2

x  3  x  3 x  4 
Identify the LCD.
51.
52.
53.
7 3
,
10 14
x
,
5
 x  1 x  3  x  3 x  4
2x
3
, 2
x  9 x  4x  3
2
Find the LCD then convert each expression to an equivalent expression with the denominator equal to the LCD.
On #55 and #56 multiply out the numerators of your equivalent expression but NOT the denominators!
54.
5
6b
,
2
4ab 3ab
55.
6
,
5
56.
 x  3 x  4  x  4 x  1
2.4 Addition and Subtraction of Rational Expressions.
Add or subtract the expressions with like denominators, simplify as much as possible
57.
2b  1
5

b3 b3
58.
x2
5x  6

x6 x6
x2 x4
,
x  3 x 1
Add or subtract the expressions with unlike denominators, simplify as much as possible.
59.
61.
63.
5
7

2 x  3x 4 x  6
2
2
5
 2
y  3 y  4 y  16
2
a 1
3
 2
9a  6a  8 3a  2a  8
2
60.
3y
6  2y

2 y y2
62.
2 y 1
2y 3
 2
4 y 1 4 y  9 y  2
2.5 Rational Equations.
Solve the rational equations. Be sure to check all solutions. If a solution does not check state that it is extraneous.
64.
w w3
3


5
w
w
66.
x
1
2

 2
x  2 x  4 x  6x  8
65.
x
1
x 8


x2 x4 x2
Solve the following proportions.
67.
5 3

x 12
68.
x 1 3

2x 5
69.
9
2

3x  1 x
2.6 Applications of Rational Equations and Proportions
70. A lawn fertilizer calls for 2 pounds for 150 square feet. At this rate, how many pounds are required for 825 square feet?
71. A map has a scale of 20 miles equals 1 inch. How many inches will two cities be apart on the map if they are actually 140 miles
apart?
72. Jess answered 8 of 10 trivia questions correct. At this rate how many questions out of 250 will she answer correctly?
73. A boat travels 10 miles upstream against the current in the same time it takes to go 30 miles downstream with the current. If the
speed of the current is 2 miles per hour, find the speed of the boat in still water.
74. A plane flies 400 miles with the wind in the same time it takes to fly 320 miles against the wind. If the speed of the wind is 20
miles per hour, find the speed of the plane in still air.