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

By Earl Swokowski, Jeffery A. Cole

The most recent 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 obvious, the time-tested workout units function numerous functions, its uncluttered structure is attractive, and the trouble point of difficulties is acceptable and constant. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, vintage version, 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 Edition

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1–2: If x < 0 and y > 0, determine the sign of the real number. 1 (a) xy (b) x y x ϩx (c) y x y (b) xy 2 (c) 2 (a) 2 (d) y Ϫ x xϪy xy (d) y͑ y Ϫ x͒ Exer. 3–6: Replace the symbol ᮀ with either <, >, or ‫ ؍‬to make the resulting statement true. 4 ᮀ␲ (f ) The negative of z is not greater than 3. (g) The quotient of p and q is at most 7. (h) The reciprocal of w is at least 9. (i) The absolute value of x is greater than 7. 8 (a) b is positive. (b) s is nonpositive. (c) w is greater than or equal to Ϫ4.

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 ?

48 ϫ 10Ϫ4 Many calculators use scientific form in their display panels. For the number c ϫ 10n, the 10 is suppressed and the exponent is often shown preceded by the letter E. For example, to find ͑4,500,000͒2 on a scientific calculator, we could enter the integer 4,500,000 and press the x 2 (or squaring) key, obtaining a display similar to one of those in Figure 6. 025 ϫ 1013. Thus, ͑4,500,000͒2 ϭ 20,250,000,000,000. Calculators may also use scientific form in the entry of numbers. The user’s manual for your calculator should give specific details.

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