Math4
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math4.rtf[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]
[INSERT TITLE HERE]
Student Name
Allied American University
Author Note
This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.
1. Find the greatest common factor. 4, 6, 12.
2. Factor. 24x3 + 30x2
3. Factor out the GCF with a negative coefficient. –24m2n6 – 8mn5 – 32n4
4. Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y
5. The GCF of 15y + 20 is 5. The GCF of 15y + 21 is 3. Find the GCF of the product (15y + 20)(15y + 21).
6. The area of a rectangle of length x is given by 15x – x2. Find the width of the rectangle in terms of x.
7. Factor the trinomial completely. x2 + 8x – 9
8. Factor the trinomial completely. 2x2 + 16x + 32
9. Complete the following statement. 6a2 – 5a + 1 = (3a – 1)(__?__)
10. State whether the following is true or false. x2 – 7x – 30 = (x + 3)(x – 10)
11. Factor completely. x2 + 11x + 28
12. Factor completely. 15x2 + 23x + 4
13. Factor completely. 6z3 – 27z2 + 12z
14. The number of hot dogs sold at the concession stand during each hour iih after opening at a soccer tournament is given by the polynomial 2h2 – 19h + 24. Write this polynomial in factored form.
15. Find a positive value for k for which the polynomial can be factored. x2 – kx + 29
16. Factor completely. 9x2 + 4
17. Determine whether the following trinomial is a perfect square. If it is, factor the binomial.x2 – 12x + 36
18. Factor completely. 25x2 + 40xy + 16y2
19. Factor. s2(t – u) – 9t2(t – u)
20. State which method should be applied as the first step for factoring the polynomial. 6x3 + 9x
21. State which method should be applied as the first step for factoring the polynomial. 2a2 + 9a + 10
22. Solve the quadratic equation. 5x2 + 17x = –6
23. Solve the quadratic equation. 3x(2x – 15) = –84
24. The sum of an integer and its square is 30. Find the integer.
25. If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?
26. Write in simplest form.
8
14
9
27
x
x
27. Write in simplest form.
2
2
– 6+ 8
16
xx
x
-
28. Write the expression in simplest form.
4 – 8 + 32
4 – 2 + 8
zyzy
yzzy
-
-
29. The area of the rectangle is represented by 5x2 + 19x + 12. What is the length?
5x + 4
30. Multiply.
3
8
98
2
x
x
×
31. Multiply.
2
3127
– 54
xx
xxx
-
×
-
32. Divide.
26515
2112
xx
--
¸
33. Divide.
(
)
22
2
2
4
+ 2
6– 12
xy
xxy
xxy
-
¸
34. Perform the indicated operations.
22
22
– 9368
4 – 244 – 36 + 5 – 6
xxxx
xxxxx
-
××
35. Find the area of the rectangle shown.
36. Subtract. Express your answer in simplest form.
7
2020
xx
-
37. Subtract. Express your answer in simplest form.
312
44
x
xx
-
--
38. Add. Express your answer in simplest form.
2
3 – 70
– 7– 7
xx
xx
+
39. Add. Express your answer in simplest form.
2
810
ss
+
40. Add or subtract as indicated.
2
112
+ 6 – 636
r
rrr
-+
-
41. One number is 8 less than another. Let x represent the larger number and use a rational expression to represent the sum of the reciprocals of the two numbers.
42. Simplify.
8
20
4
6
43. Simplify.
10
30
a
b
b
-
44. What values for x, if any, must be excluded in the following algebraic fraction?
– 2
7
x
45. What values for x, if any, must be excluded in the following algebraic fraction?
2
2
914
x
xx
+
-+
46. Solve for x.
5
x
+ 6 = 1
47. Solve for x.
3
+ 5
– 3– 3
x
xx
=
48. Solve for x.
26
7
x
=
49. One number is 3 times another. If the sum of their reciprocals is
2
9
, find the two numbers.
50. A 5-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 16 feet?
A. This week we will be discussing about factoring polynomials.
How do we factor a difference of two squares? Please give an example of factoring a difference of two squares. Please show all of your work to arrive at the final answer. Then, present a math problem for your classmates to solve
