March 7, 2017

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

By Earl Swokowski, Jeffery A. Cole

The newest variation 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 apparent, the time-tested workout units function quite a few functions, its uncluttered structure is beautiful, and the trouble point of difficulties is suitable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage version, 12E, successfully prepares scholars for extra classes in arithmetic via its first-class, time-tested challenge units

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4 Fractional Expressions 45 An alternative method is to multiply the numerator and denominator of the given expression by ͑x ϩ 3͒͑a ϩ 3͒, the lcd of the numerator and denominator, and then simplify the result. L Some quotients that are not rational expressions contain denominators of the form a ϩ 2b or 2a ϩ 2b; as in the next example, these quotients can be simplified by multiplying the numerator and denominator by the conjugate a Ϫ 2b or 2a Ϫ 2b, respectively. Of course, if a Ϫ 2b appears, multiply by a ϩ 2b instead.

ILLUS TRATION Canceled Common Factors ad a ϭ bd b pqr q ϭ rpv v mn m ϭ npq pq A rational expression is simplified, or reduced to lowest terms, if the numerator and denominator have no common polynomial factors of positive degree and no common integral factors greater than 1. To simplify a rational expression, we factor both the numerator and the denominator into prime factors and then, assuming the factors in the denominator are not zero, cancel common factors, as in the following illustration.

Hence, 4ac ϩ 2bc Ϫ 2ad Ϫ bd ϭ 2c͑2a ϩ b͒ Ϫ d͑2a ϩ b͒ ϭ ͑2c Ϫ d͒͑2a ϩ b͒. 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 ?

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