Beginning Algebra, 11th Edition

43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. ...

For example, The following conditions must be true for a binomial to be a difference of squares. 1.Both terms of the binomial mu ...

382 CHAPTER 6 Factoring and Applications Factoring Differences of Squares Factor each difference of squares. (a) (b) Write each ...

On the one hand, a necessary condition for a trinomial to be a perfect square is that two of its terms be perfect squares.For th ...

(b) Twice First Last term term (c) The first and last terms are perfect squares. and Twice the product of the first and last ter ...

Notice the pattern of the terms in the factored form of (a binomial factor)(a trinomial factor) The binomial factor has the dif ...

OBJECTIVE 4 Factor a sum of cubes. A sum of squares, such as cannot be factored by using real numbers, but a sum of cubescan. m^ ...

The methods of factoring discussed in this section are summarized here. SECTION 6.4 Special Factoring Techniques 387 Special Fac ...

19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.Concept Check When a student was directed to factor from Exercise 30com- plet ...

Although we usually factor polynomials using integers, we can apply the same concepts to factoring using fractions and decimals. ...

390 CHAPTER 6 Factoring and Applications Match each polynomial in Column I with the best choice for factoring it in Column II. T ...

Summary Exercises on Factoring^391 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 8 ...

392 CHAPTER 6 Factoring and Applications OBJECTIVES Galileo Galilei developed theories to explain physical phenomena and set up ...

The original equation, has two solutions, and Check these solutions by substituting for xin this equation. Then start overand su ...

Solving a Quadratic Equation with a Common Factor Solve Standard form Factor out 2. Divide each side by 2. Factor. Zero-factor p ...

SECTION 6.5 Solving Quadratic Equations by Factoring^395 CAUTION A common error is to include the common factor 2 as a solution ...

Solving Quadratic Equations with Double Solutions Solve each equation. (a) Factor the perfect square trinomial. Zero-factor prop ...

Checkby substituting, in turn, 0, and 1 into the original equation. The solution set is (b) Factor Zero-factor property or or So ...

6.Concept Check Identify each equation as linearor quadratic. (a) (b) (c) (d) 7.Students often become confused as to how to hand ...

69. 70. 71. 72. Brain Busters Solve each equation, and check your solutions. Galileo’s formula describing the ...