By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Those authors have created a e-book to truly support scholars visualize arithmetic for greater comprehension. by way of developing algebraic visible side-by-sides to resolve numerous difficulties within the examples, the authors exhibit scholars the connection of the algebraic answer with the visible, frequently graphical, answer. additionally, the authors have extra numerous new instruments to aid scholars greater use the booklet for max effectiveness not to simply move the path, yet actually comprehend the material.
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Additional info for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
A2 Ϫ B 2 ͑A ϩ B͒ ͑A Ϫ B͒ EXAMPLE 8 Factor each of the following. a) x 2 Ϫ 16 b) 9a2 Ϫ 25 c) 6x 4 Ϫ 6y 4 Solution a) x 2 Ϫ 16 x 2 Ϫ 42 ͑x ϩ 4͒ ͑x Ϫ 4͒ b) 9a2 Ϫ 25 ͑3a͒2 Ϫ 52 ͑3a ϩ 5͒ ͑3a Ϫ 5͒ c) 6x 4 Ϫ 6y 4 6͑x 4 Ϫ y 4 ͒ 6͓͑x 2 ͒2 Ϫ ͑ y 2 ͒2 ͔ 6͑x 2 ϩ y 2 ͒ ͑x 2 Ϫ y 2 ͒ x2 ؊ y2 can be factored 6͑x 2 ϩ y 2 ͒ ͑x ϩ y͒ ͑x Ϫ y͒ further. Because none of these factors can be factored further, we have factored completely. The rules for squaring binomials can be reversed to factor trinomials that are squares of binomials: A2 ϩ 2AB ϩ B 2 ͑A ϩ B͒2; A2 Ϫ 2AB ϩ B 2 ͑A Ϫ B͒2.
QXP 24 Chapter R 12/2/04 2:42 PM Page 24 • Basic Concepts of Algebra The factorization of y 2 Ϫ 7y ϩ 12 is ͑ y Ϫ 3͒ ͑ y Ϫ 4͒. We must also include the common factor that we factored out earlier. Thus we have 2y 2 Ϫ 14y ϩ 24 2͑ y Ϫ 3͒ ͑ y Ϫ 4͒. EXAMPLE 5 Factor: x 4 Ϫ 2x 3 Ϫ 8x 2. Solution First, we look for a common factor. Each term has a factor of x 2, so we factor it out first: x 4 Ϫ 2x 3 Ϫ 8x 2 x 2͑x 2 Ϫ 2x Ϫ 8͒. Now we consider the trinomial x 2 Ϫ 2x Ϫ 8. We look for two numbers whose product is Ϫ8 and whose sum is Ϫ2.
24 5͑2t ϩ 5͒ 1 Ϫ 10 23. 5y Ϫ ͑2y Ϫ 10͒ 25 5 22. 9 4͑3y Ϫ 2͒ 12 5 17 12 24. 8x Ϫ ͑3x Ϫ 5͒ 40 25. 7͑3x ϩ 6͒ 11 Ϫ ͑x ϩ 2͒ 7 Ϫ 3 2 26. 9͑2x ϩ 8͒ 20 Ϫ ͑x ϩ 5͒ Ϫ3 27. 4͑3y Ϫ 1͒ Ϫ 6 5͑ y ϩ 2͒ 28. 3͑2n Ϫ 5͒ Ϫ 7 4͑n Ϫ 9͒ 29. x 2 ϩ 3x Ϫ 28 0 Ϫ7, 4 20 7 Ϫ7 30. y 2 Ϫ 4y Ϫ 45 0 Ϫ5, 9 10 Ϫ2 5 37. x 2 Ϫ 4x Ϫ 32 0 38. t 2 ϩ 12t ϩ 27 0 39. 3y 2 ϩ 8y ϩ 4 0 40. 9y 2 ϩ 15y ϩ 4 0 Ϫ4, 8 41. 12z 2 ϩ z 6 Ϫ 43. 12a2 Ϫ 28 5a Ϫ9, Ϫ3 3 2 5 42. 6x 2 Ϫ 7x 10 Ϫ , 2 , 4 3 6 44. 21n2 Ϫ 10 n 45.