By Raymond A.;Ziegler, Michael R.;Byleen, K Barnet

The Barnett/Ziegler/Byleen/Sobecki collage Algebra sequence is designed to offer scholars a superb grounding in pre-calculus themes in a easy demeanour. The sequence emphasizes computational talents, rules, and challenge fixing instead of idea. Explore/Discuss packing containers built-in all through every one textual content motivate scholars to imagine seriously approximately mathematical ideas. All labored examples are by way of Matched difficulties that toughen the thoughts being taught. New to those variants, expertise Connections illustrate how ideas that have been formerly defined in an algebraic context can also be solved utilizing a graphing calculator. scholars are continuously proven the underlying algebraic tools first so they don't develop into calculator-dependent. moreover, every one textual content within the sequence comprises an abundance of workouts - together with a variety of calculator-based and reasoning and writing routines - and a large choice of real-world functions illustrating how math comes in handy.

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C) Condition 3 is violated. We multiply numerator and denominator by 12x; the effect is to multiply the expression by 1, so its value is unchanged, but the denominator is left free of radicals. 6 6 12x 612x 312x ϭ ؒ ϭ ϭ x 2x 12x 12x 12x (D) Condition 4 is violated. First we convert to rational exponent form. 8x4 81ր3x4ր3 ϭ B y y1ր3 y2ր3 3 Multiply by y2ր3 ؍1. ϭ 2x4ր3y2ր3 y x 4ր3 ؍xx 1ր3 ϭ 2xx1ր3y2ր3 y Write in radical form. ϭ 2x 2xy2 y 3 MATCHED PROBLEM 7 Write in simplified radical form.

A) Ϫ(5ր2 ϩ 7ր3) (C) 21 15 ؒ 20 14 Ϫ1 (B) Ϫ(8ր17) (D) 5 ؒ (1ր2 ϩ 1ր3) Rational numbers have decimal expansions that are repeating or terminating. 625 8 The number 6 repeats indefinitely. The block 142857 repeats indefinitely. Terminating expansion Conversely, any decimal expansion that is repeating or terminating represents a rational number (see Problems 49 and 50 in Exercise R-1). The number 12 is irrational because it cannot be written in the form a͞b, where a and b are integers, b 0 (for an explanation, see Problem 89 in Section R-3).

2x(u Ϫ 3v) ϩ 5y(u Ϫ 3v) 71. 6(3x Ϫ 5)(2x Ϫ 3)2 ϩ 4(3x Ϫ 5)2(2x Ϫ 3) In Problems 29–34, factor completely, relative to the integers. 2 2 29. x ϩ 4x ϩ x ϩ 4 2 30. 2y Ϫ 6y ϩ 5y Ϫ 15 2 31. x Ϫ xy ϩ 3xy Ϫ 3y 32. 3a2 Ϫ 12ab Ϫ 2ab ϩ 8b2 33. 8ac ϩ 3bd Ϫ 6bc Ϫ 4ad In Problems 35–42, perform the indicated operations and simplify. 35. 2x Ϫ 35x ϩ 2 3x Ϫ (x ϩ 5) 4 ϩ 16 78. 15ac Ϫ 20ad ϩ 3bc Ϫ 4bd 38. (x2 Ϫ 3xy ϩ y2)(x2 ϩ 3xy ϩ y2) 79. 3x2 Ϫ 2xy Ϫ 4y2 2 39. (3u Ϫ 2v) Ϫ (2u Ϫ 3v)(2u ϩ 3v) 80. 5u2 ϩ 4uv Ϫ v2 40.