By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Those authors have created a ebook to truly aid scholars visualize arithmetic for larger comprehension. by means of developing algebraic visible side-by-sides to resolve numerous difficulties within the examples, the authors convey scholars the connection of the algebraic resolution with the visible, frequently graphical, answer. moreover, the authors have extra a number of new instruments to assist scholars greater use the booklet for max effectiveness not to in basic terms go the path, yet really comprehend the material.
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Extra resources for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
5m42 Ϫ 20 108. 2x 2 Ϫ 288 3 2 ͑ y Ϫ 3͒ ͑ y ϩ 2͒ ͑ y Ϫ 2͒ ͑x Ϫ 1͒ ͑x ϩ 1͒ 3 2 ͑ p Ϫ 2͒ ͑ p ϩ 3͒ ͑ p Ϫ 3͒ ͑x ϩ 1͒ ͑x Ϫ 1͒ 2 5͑m ϩ 2͒ ͑m Ϫ 2͒ 2 2͑x ϩ 12͒ ͑x Ϫ 12͒ 2 109. 2x 3 ϩ 6x 2 Ϫ 8x Ϫ 24 110. 3x 3 ϩ 6x 2 Ϫ 27x Ϫ 54 2͑x ϩ 3͒ ͑x ϩ 2͒ ͑x Ϫ 2͒ 3͑x ϩ 2͒ ͑x ϩ 3͒ ͑x Ϫ 3͒ 111. 4c 2 Ϫ 4cd ϩ d 2 112. 3 m6 ϩ 8m33 Ϫ 20 114. x 4 Ϫ 37x 2 ϩ 36 ͑2c Ϫ d͒ 2 ͑m ϩ 10͒ ͑m Ϫ 2͒ 115. p Ϫ 64p4 ͑3a Ϫ b͒ 2 ͑x ϩ 1͒ ͑x Ϫ 1͒ ͑x ϩ 6͒ ͑x Ϫ 6͒ 116. 125a Ϫ 8a4 p͑1 Ϫ 4p͒ ͑1 ϩ 4p ϩ 16p ͒ 2 2 118. Explain how the rule for factoring a sum of cubes can be used to factor a difference of cubes.
4. ͱ n n a ͙a n b ͙b (b 0). 5. ͙ am ͑ ͙ a ͒ . n n EXAMPLE 2 m Simplify each of the following. 6 f ) ͙ 85 ͙͑ 8 ͒ 25 32 3 5 3 41 • Radical Notation and Rational Exponents Using Property 5 g) ͙216x 5y 3 ͙36 и 6 и x 4 и x и y 2 и y Using Property 3 ͙36x 4y 2 ͙6xy ͉6x 2y͉͙6xy Using Property 1 2 6x ͉ y͉͙6xy 6x2 cannot be negative, so absoluteh) ͱ value signs are not needed for it. 2 ͙x 2 x 16 ͙16 ͉x͉ 4 Using Property 4 Using Property 1 In many situations, radicands are never formed by raising negative quantities to even powers.
EXAMPLE 1 Factor each of the following. a) 15 ϩ 10x Ϫ 5x 2 b) 12x 2y 2 Ϫ 20x 3y Solution a) 15 ϩ 10x Ϫ 5x 2 5 и 3 ϩ 5 и 2x Ϫ 5 и x 2 5͑3 ϩ 2x Ϫ x 2 ͒ We can always check a factorization by multiplying: 5͑3 ϩ 2x Ϫ x 2 ͒ 15 ϩ 10x Ϫ 5x 2. b) There are several factors common to the terms of 12x 2y 2 Ϫ 20x 3y , but 4x 2y is the “largest” of these. 12x 2y 2 Ϫ 20x 3y 4x 2y и 3y Ϫ 4x 2y и 5x 4x 2y͑3y Ϫ 5x͒ Factoring by Grouping In some polynomials, pairs of terms have a common binomial factor that can be removed in a process called factoring by grouping.