Download e-book for kindle: Algebra and Trigonometry with Analytic Geometry, Classic by Earl Swokowski, Jeffery A. Cole

By Earl Swokowski, Jeffery A. Cole

ISBN-10: 0495559717

ISBN-13: 9780495559719

The newest version within the hugely revered Swokowski/Cole precalculus sequence keeps the weather that experience made it so well liked by teachers and scholars alike: its exposition is obvious, the time-tested workout units function quite a few purposes, its uncluttered structure is attractive, and the trouble point of difficulties is acceptable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage variation, 12E, successfully prepares scholars for additional classes in arithmetic via its very good, time-tested challenge units.

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Extra resources for Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition

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Note that if we factor 2ck Ϫ dk as k͑2c Ϫ d͒, then the last expression is ͑2a ϩ b͒͑2c Ϫ d͒. 3 39 Exercises 43 ͑2x ϩ y Ϫ 3z͒2 Exer. 1–44: Express as a polynomial. 44 ͑x Ϫ 2y ϩ 3z͒2 1 ͑3x ϩ 4x Ϫ 7x ϩ 1͒ ϩ ͑9x Ϫ 4x Ϫ 6x͒ 3 2 3 2 Exer. 45–102: Factor the polynomial. 2 ͑7x 3 ϩ 2x 2 Ϫ 11x͒ ϩ ͑Ϫ3x 3 Ϫ 2x 2 ϩ 5x Ϫ 3͒ 3 ͑4x 3 ϩ 5x Ϫ 3͒ Ϫ ͑3x 3 ϩ 2x 2 ϩ 5x Ϫ 7͒ 4 ͑6x Ϫ 2x ϩ x Ϫ 2͒ Ϫ ͑8x Ϫ x Ϫ 2͒ 3 2 46 4u2 Ϫ 2uv 47 3a2b2 Ϫ 6a2b 48 10xy ϩ 15xy2 49 3x 2y 3 Ϫ 9x 3y 2 50 16x 5y 2 ϩ 8x 3y 3 51 15x 3y 5 Ϫ 25x 4y 2 ϩ 10x 6y 4 52 121r 3s4 ϩ 77r 2s4 Ϫ 55r 4s3 53 8x 2 Ϫ 53x Ϫ 21 54 7x 2 ϩ 10x Ϫ 8 55 x 2 ϩ 3x ϩ 4 56 3x 2 Ϫ 4x ϩ 2 57 6x 2 ϩ 7x Ϫ 20 58 12x 2 Ϫ x Ϫ 6 59 12x 2 Ϫ 29x ϩ 15 60 21x 2 ϩ 41x ϩ 10 61 4x 2 Ϫ 20x ϩ 25 62 9x 2 ϩ 24x ϩ 16 63 25z2 ϩ 30z ϩ 9 64 16z2 Ϫ 56z ϩ 49 65 45x 2 ϩ 38xy ϩ 8y 2 66 50x 2 ϩ 45xy Ϫ 18y 2 67 36r 2 Ϫ 25t 2 68 81r 2 Ϫ 16t 2 69 z4 Ϫ 64w 2 70 9y4 Ϫ 121x 2 71 x 4 Ϫ 4x 2 72 x 3 Ϫ 25x 2 5 ͑2x ϩ 5͒͑3x Ϫ 7͒ 6 ͑3x Ϫ 4͒͑2x ϩ 9͒ 7 ͑5x ϩ 7y͒͑3x ϩ 2y͒ 8 ͑4x Ϫ 3y͒͑x Ϫ 5y͒ 9 ͑2u ϩ 3͒͑u Ϫ 4͒ ϩ 4u͑u Ϫ 2͒ 10 ͑3u Ϫ 1͒͑u ϩ 2͒ ϩ 7u͑u ϩ 1͒ 11 ͑3x ϩ 5͒͑2x 2 ϩ 9x Ϫ 5͒ 12 ͑7x Ϫ 4͒͑x 3 Ϫ x 2 ϩ 6͒ 13 ͑t ϩ 2t Ϫ 5͒͑3t Ϫ t ϩ 2͒ 2 2 14 ͑r 2 Ϫ 8r Ϫ 2͒͑Ϫr 2 ϩ 3r Ϫ 1͒ 15 ͑x ϩ 1͒͑2x Ϫ 2͒͑x ϩ 5͒ 16 ͑2x Ϫ 1͒͑x Ϫ 5͒͑x Ϫ 1͒ 8x y Ϫ 10x y 17 2x 2y 6a3b3 Ϫ 9a2b2 ϩ 3ab4 18 3ab2 2 2 3 19 45 rs ϩ 4st 3 3 3u3v4 Ϫ 2u5v2 ϩ ͑u2v2͒2 u3v2 2 20 3 6x2yz3 Ϫ xy2z xyz 21 ͑2x ϩ 3y͒͑2x Ϫ 3y͒ 22 ͑5x ϩ 4y͒͑5x Ϫ 4y͒ 73 x 2 ϩ 25 74 4x 2 ϩ 9 23 ͑x 2 ϩ 2y͒͑x 2 Ϫ 2y͒ 24 ͑3x ϩ y 3͒͑3x Ϫ y 3͒ 75 75x 2 Ϫ 48y 2 76 64x 2 Ϫ 36y 2 25 ͑x 2 ϩ 9͒͑x 2 Ϫ 4͒ 26 ͑x 2 ϩ 1͒͑x 2 Ϫ 16͒ 77 64x 3 ϩ 27 78 125x 3 Ϫ 8 27 ͑3x ϩ 2y͒2 28 ͑5x Ϫ 4y͒2 79 64x 3 Ϫ y6 80 216x9 ϩ 125y3 29 ͑x 2 Ϫ 3y 2͒2 30 ͑2x 2 ϩ 5y 2͒2 81 343x 3 ϩ y9 82 x 6 Ϫ 27y 3 31 ͑x ϩ 2͒2͑x Ϫ 2͒2 32 ͑x ϩ y͒2͑x Ϫ y͒2 83 125 Ϫ 27x 3 84 x 3 ϩ 64 85 2ax Ϫ 6bx ϩ ay Ϫ 3by 86 2ay2 Ϫ axy ϩ 6xy Ϫ 3x 2 87 3x 3 ϩ 3x 2 Ϫ 27x Ϫ 27 88 5x 3 ϩ 10x 2 Ϫ 20x Ϫ 40 35 ͑x1/3 Ϫ y1/3͒͑x 2/3 ϩ x1/3y1/3 ϩ y 2/3͒ 89 x 4 ϩ 2x 3 Ϫ x Ϫ 2 90 x 4 Ϫ 3x 3 ϩ 8x Ϫ 24 36 ͑x1/3 ϩ y1/3͒͑x 2/3 Ϫ x1/3y1/3 ϩ y 2/3͒ 91 a3 Ϫ a2b ϩ ab2 Ϫ b3 92 6w8 ϩ 17w4 ϩ 12 37 ͑x Ϫ 2y͒3 38 ͑x ϩ 3y͒3 93 a6 Ϫ b6 94 x 8 Ϫ 16 39 ͑2x ϩ 3y͒3 40 ͑3x Ϫ 4y͒3 95 x 2 ϩ 4x ϩ 4 Ϫ 9y2 96 x 2 Ϫ 4y 2 Ϫ 6x ϩ 9 41 ͑a ϩ b Ϫ c͒2 42 ͑x 2 ϩ x ϩ 1͒2 97 y 2 Ϫ x 2 ϩ 8y ϩ 16 98 y 2 ϩ 9 Ϫ 6y Ϫ 4x 2 33 34 ͑ 2x ϩ 2y ͒͑ 2x Ϫ 2y ͒ ͑ 2x ϩ 2y ͒2͑ 2x Ϫ 2y ͒2 40 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA 99 y 6 ϩ 7y 3 Ϫ 8 100 8c6 ϩ 19c3 Ϫ 27 101 x16 Ϫ 1 Exercise 104 x 102 4x 3 ϩ 4x 2 ϩ x I ?

2 Exponents and Radicals 17 If m and n are positive integers, then m factors of a ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ aman ϭ a и a и a и и и и и a и a и a и a и и и и и a. n factors of a Since the total number of factors of a on the right is m ϩ n, this expression is equal to amϩn; that is, aman ϭ amϩn. We can extend this formula to m Յ 0 or n Յ 0 by using the definitions of the zero exponent and negative exponents. This gives us law 1, stated in the next chart. To prove law 2, we may write, for m and n positive, ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ ͑am͒n ϭ am и am и am и и и и и am n factors of am and count the number of times a appears as a factor on the right-hand side.

ILLUS TRATION The Exponential Notation an 54 ϭ 5 и 5 и 5 и 5 ϭ 625 ͑ 12 ͒5 ϭ 12 и 12 и 12 и 12 и 12 ϭ 321 ͑Ϫ3͒3 ϭ ͑Ϫ3͒͑Ϫ3͒͑Ϫ3͒ ϭ Ϫ27 ͑Ϫ 31 ͒4 ϭ ͑Ϫ 31 ͒͑Ϫ 31 ͒͑Ϫ 31 ͒͑Ϫ 31 ͒ ϭ ͑ 19 ͒͑ 19 ͒ ϭ 811 It is important to note that if n is a positive integer, then an expression such as 3an means 3͑an͒, not ͑3a͒n. The real number 3 is the coefficient of an in the expression 3an. Similarly, Ϫ3an means ͑Ϫ3͒an, not ͑Ϫ3a͒n. ILLUS TRATION The Notation can 5 и 23 ϭ 5 и 8 ϭ 40 Ϫ5 и 23 ϭ Ϫ5 и 8 ϭ Ϫ40 Ϫ24 ϭ Ϫ͑24͒ ϭ Ϫ16 3͑Ϫ2͒3 ϭ 3͑Ϫ2͒͑Ϫ2͒͑Ϫ2͒ ϭ 3͑Ϫ8͒ ϭ Ϫ24 We next extend the definition of an to nonpositive exponents.

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Algebra and Trigonometry with Analytic Geometry, Classic 12th Edition by Earl Swokowski, Jeffery A. Cole


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