Module 4

Beginning Algebra
Allied American University

Author Note This paper was prepared for MAT110, Module 4 Homework Assignment

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

2. Factor. 24x3 + 30x2 = 6x(4x^2+5x)

3. Factor out the GCF with a negative coefficient. –24m2n6 – 8mn5 – 32n4

GFC= 8n^4 = -8n^4(3m^2n^2+n^+4)

4. Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y =(x+1) (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). =15

6. The area of a rectangle of length x is given by 15x – x2. Find the width of the rectangle in terms of x. w=15-x

7. Factor the trinomial completely. x2 + 8x – 9 = (x-1) (x+9)

8. Factor the trinomial completely. 2x2 + 16x + 32 = (2x+8) (x+4)

9. Complete the following statement. 6a2 – 5a + 1 = (3a – 1)(__?__) = (2a-1)

10. State whether the following is true or false. x2 – 7x – 30 = (x + 3)(x – 10) = True

11. Factor completely. x2 + 11x + 28 = (x+4) (x+7)

12. Factor completely. 15x2 + 23x + 4 = (5x+1) (3x+4)

13. Factor completely. 6z3 – 27z2 + 12z = 3z(z-4) (2z-1)

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. = (2h-3) (h-8)

15. Find a positive value for k for which the polynomial can be factored. x2 – kx + 29 = (x=1) (x-29) k = 30

16. Factor completely. 9x2 + 4 = 9x^2+4

17. Determine whether the following trinomial is a perfect square. If it is, factor the binomial.x2 – 12x + 36 = (x-6) (x-6)

18. Factor completely. 25x2 + 40xy + 16y2

(5x+4y) (5x+4y)

19. Factor. s2(t – u) – 9t2(t – u) = (5^2-9t^2) (t-u)

20. State which method should be applied as the first step for factoring the polynomial. 6x3 + 9x = 3x factor out GCF

21. State which method should be applied as the first step for factoring the polynomial. 2a2 + 9a + 10 = Factor product of binomial

22. Solve the quadratic equation. 5x2 + 17x = –6 = (5x+2) (x+3)

23. Solve the quadratic equation. 3x(2x – 15) = –84 = (2x-7) (3x-12)

24. The sum of an integer and its square is 30. Find the integer. = x=5

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? = 15cm x15cm

26. Write in simplest form. =1/3x^6

27. Write in simplest form. =(x-2)/(x+4)

28. Write the expression in simplest form. = = -2+8/z-2

29. The area of the rectangle is represented by 5x2 + 19x + 12. What is the length? L=5x+3
5x + 4

30. Multiply. = 36/x^5

31. Multiply. = -21/x-5

32. Divide. = =8/35

33. Divide. = 1/6x

34. Perform the indicated operations. = 8x/16x-17

35. Find the area of the rectangle shown. = 12x+w/x-7 36. Subtract. Express your answer in simplest form. = 3x/10

37. Subtract. Express your answer in simplest form. = 3

38. Add. Express your answer in simplest form. =x+10

39. Add. Express your answer in simplest form. = 8s+10/s^2

40. Add or subtract as indicated. = 2/r+6

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. 1/x + 1/x=8

42. Simplify. = 8/10

43. Simplify. = -a+10b/30

44. What values for x, if any, must be excluded in the following algebraic fraction? None

45. What values for x, if any, must be excluded in the following algebraic fraction? X=2 or x=7

46. Solve for x. + 6 = 1 = -25

47. Solve for x. = x=3

48. Solve for x. = 21=x

49. One number is 3 times another. If the sum of their reciprocals is , find the two numbers. = 3x=18

50. A 5-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 16 feet? 20 Ft