By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Those authors have created a ebook to actually support scholars visualize arithmetic for higher comprehension. through developing algebraic visible side-by-sides to resolve quite a few difficulties within the examples, the authors exhibit scholars the connection of the algebraic answer with the visible, frequently graphical, resolution. additionally, the authors have additional numerous new instruments to aid scholars larger use the ebook for max effectiveness not to basically go the direction, yet actually comprehend the material.
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Extra resources for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
1 xϩy cϪ2 xϪyϪz xϩyϩz Add or subtract and, if possible, simplify. 5 1 3 10 4 23. ϩ 24. Ϫ 2x 2x x 9y 9y 25. 27. 3 2a ϩ 1 2a ϩ 3 2a ϩ 3 5 3 Ϫ 4z 8z 7 8z 26. 28. 2 3y 29. 3 2 ϩ x ϩ 2 x2 Ϫ 4 3x Ϫ 4 ͑x ϩ 2͒ ͑x Ϫ 2͒ 30. 5 2 Ϫ a Ϫ 3 a2 Ϫ 9 5a ϩ 13 ͑a ϩ 3͒ ͑a Ϫ 3͒ 31. Ϫy ϩ 10 y 2 Ϫ y 2 Ϫ y Ϫ 20 y ϩ 4 ͑ y ϩ 4͒ ͑ y Ϫ 5͒ 32. 5 6 Ϫ5y Ϫ 9 Ϫ y 2 ϩ 6y ϩ 9 y ϩ 3 ͑ y ϩ 3͒2 3 x Ϫ 5y 33. ϩ x ϩ y x2 Ϫ y2 34. 35. ) Simplify. x2 Ϫ y2 xy 47. xϪy y y x Ϫ y x 49. 1 1 ϩ y x 8 c2 51. 2 1ϩ c cϩ 53. y ͑ y Ϫ 2͒ ͑ y Ϫ 3͒ 5a2 ϩ 10ab Ϫ 4b 2 ͑a ϩ b͒ ͑a Ϫ b͒ 3 2ϩx xϩy x aϪb a b 48.
The positive root is called the principal root. When an expression such as ͙4 or 6 ͙ 23 is used, it is understood to represent the principal (nonnegative) 6 root. To denote a negative root, we use Ϫ͙4, Ϫ͙ 23, and so on. GCM EXAMPLE 1 Simplify each of the following. d) ͱ 5 3 b) Ϫ͙36 a) ͙36 32 243 c) ͙ Ϫ8 4 e) ͙ Ϫ16 Solution a) ͙36 6, because 62 36. b) Ϫ͙36 Ϫ6, because 62 36 and Ϫ͑ ͙36 ͒ Ϫ͑6͒ Ϫ6. 3 c) ͙ Ϫ8 Ϫ2, because ͑Ϫ2͒3 Ϫ8. d) ͱ 5 2 32 , because 243 3 ͩͪ 2 3 5 25 32 . 35 243 4 e) ͙ Ϫ16 is not a real number, because we cannot find a real number that can be raised to the fourth power to get Ϫ16.
PAIRS OF FACTORS SUMS OF FACTORS 1, Ϫ24 Ϫ1, Ϫ23 24 23 2, Ϫ12 Ϫ10 Ϫ2, 12 10 3, Ϫ8 Ϫ5 Ϫ3, 8 5 4, Ϫ6 Ϫ2 Ϫ4, 6 ؊3 ؒ 8 ؍؊24 ; ؊3 ؉ 8 ؍5 2 4. Split the middle term using the numbers found in step (3): 5x Ϫ3x ϩ 8x . 5. Finally, factor by grouping: 6x 2 ϩ 5x Ϫ 4 6x 2 Ϫ 3x ϩ 8x Ϫ 4 3x͑2x Ϫ 1͒ ϩ 4͑2x Ϫ 1͒ ͑2x Ϫ 1͒ ͑3x ϩ 4͒. Be sure to include the common factor to get the complete factorization of the original trinomial: 12x 3 ϩ 10x 2 Ϫ 8x 2x͑2x Ϫ 1͒ ͑3x ϩ 4͒. QXP 12/2/04 2:42 PM Page 27 Section R.
Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series) by Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger