Module 4 homework assignment

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Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

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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 h 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

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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

x x x −

28. Write the expression in simplest form. 4 – 8 + 32

4 – 2 + 8 z yz y yz z y − −

29. The area of the rectangle is represented by 5x2 + 19x + 12. What is the length?

5x + 4

30. Multiply. 3

8

9 8 2 x

x ⋅

31. Multiply. 2 3 12 7

– 5 4 x x

x x x −

⋅ −

32. Divide. 2 6 5 15

21 12 x x− −

÷

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33. Divide. ( ) 2 2

2 2

4 + 2

6 – 12 x y

x xy x xy −

÷

34. Perform the indicated operations. 2 2

2 2

– 9 36 8 4 – 24 4 – 36 + 5 – 6 x x x x x x x x x

− ⋅ ⋅

35. Find the area of the rectangle shown.

36. Subtract. Express your answer in simplest form.

7 20 20

x x −

37. Subtract. Express your answer in simplest form.

3 12 4 4

x x x

− − −

38. Add. Express your answer in simplest form.

2 3 – 70 – 7 – 7 x x

x x +

39. Add. Express your answer in simplest form.

2

8 10 s s +

40. Add or subtract as indicated. 2 1 1 2

+ 6 – 6 36 r

r r r − +

−

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

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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 9 14

x x x

+ − +

46. Solve for x. 5 x

+ 6 = 1

47. Solve for x. 3

+ 5 – 3 – 3 x

x x =

48. Solve for x. 2 6 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?