Assignment #1 MAT11 Summer 015 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. Tuesday May 6 th (see your syllabus for late penalty!). 1.1 Greatest Common Factor 1. Factor out the GCF. 14x 3 7x + 7x. Factor out a (-1) from the polynomial. 3 x Factor each polynomial by factoring out the opposite of the GCF. 3. -4x 3 + 1x 4. -1x 3 + 4x 8x 5. 6 3z 1. Factoring Trinomials of the Form x + bx + c Factor each trinomial state if a polynomial is prime. 6. y 10y +16 7. x + x 0 8. c + 1c + 0 9. 10. x + x + 3 Factor each trinomial. Make sure to factor out a negative and/or the GCF where applicable. 11. 3x +1x 36 1. -x 3 10x + 1x 13. -x 7x 10
1.3 Factoring Trinomials in the Form ax + bx + c where a 1 Factor (if a polynomial is prime say so) 14. 3x + 10x + 7 15. b 15b + 7 16. 6y 7y 5 Factor. Make sure to factor out a negative and/or the GCF where applicable. 17. 0x 3 18x + 4x 18. -16x + 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. 5a 81 0. x 3 64x 1. x 4 16. x + 4 3. b 3 + 7 4. x 3 64 5. 16x 3 + 54
1.5 Solving Quadratic Equations by Factoring Solve each equation. 6. (x 1)(3x+4) = 0 7. x(x 1)(x+) = 0 8. x 14x + 45 = 0 9. 5x 16 = 0 30. 4x + x 6 = 0 31. 5x 0 = 0 3. (x )(x 3)= 6 33. x(x 3) + = 30 34. x(x 3) = 5x(x 4) +8
.1 Introduction to Rational Expressions Substitute the given number into the expression and simplify (if possible). 35. x x 3 4x1 let x 3 36. a1a a3a4 let a 3 Write the domain of the expression using words and in interval notation. 37. y y 4 5y6 38. x 1 x Reduce the expression to lowest terms. 39. 0xy 16 3 5 xy 40. 10m 3 m m 1 3 1 41. 10x 0 x 4 4. y y6 y y 43. 3x 6 1 6x
. Multiplication and Division of Rational Expressions Multiply or divide as indicated. 44. 3 30 10 5 45. 3x 1 3x 6x 4x 8 46. 4a16 a4 3a15 a10 47. p p 1 16 p 1 4 p1 p 1 48. x 5x 1 x 3x 9 3x 8x 16 3x 13x 1.3 Least Common Denominator Fill in the blank to convert the expressions to equivalent expressions with the indicated denominator. 49. 11 33 50. x x 3 x 3 x 4
Identify the LCD. 51. 7 3 10 14 5. x x 1 x 3 x 3 x 4 5 53. x 3 9 4 3 x x x 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 ab 4ab 3 6 5 55. x 3 x 4 x 4 x 1 56. x x4 x3 x1.4 Addition and Subtraction of Rational Expressions. Add or subtract the expressions with like denominators simplify as much as possible 57. b 1 5 b3 b3 58. x 5x 6 x6 x 6
Add or subtract the expressions with unlike denominators simplify as much as possible. 59. 5 7 x 3x 4x 6 60. 3y 6 y y y 61. 5 y 3y 4 y 16 6. y1 y3 4y 1 4y 9y 63. a 1 3 9a 6a 8 3a a 8
.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 65. 5 w w x 1 x8 x x 4 x 66. x 1 x x x x 4 6 8 Solve the following proportions. 67. 5 3 x 1 68. x 1 3 9 69. x 5 3x1 x
.6 Applications of Rational Equations and Proportions 70. A lawn fertilizer calls for pounds for 150 square feet. At this rate how many pounds are required for 85 square feet? 71. A map has a scale of 0 miles equals 1 inch. How many inches will two cities be apart on the map if they are actually 140 miles apart? 7. Jess answered 8 of 10 trivia questions correct. At this rate how many questions out of 50 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 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 30 miles against the wind. If the speed of the wind is 0 miles per hour find the speed of the plane in still air.