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 obvious, the time-tested workout units characteristic a number of functions, its uncluttered structure is beautiful, 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 extra classes in arithmetic via its first-class, time-tested challenge units

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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. 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.

11 (a) ͑Ϫ5͉͒ 3 Ϫ 6 ͉ (b) ͉ Ϫ6 ͉͑͞Ϫ2͒ (c) ͉ Ϫ7 ͉ ϩ ͉ 4 ͉ (e) t is not less than 5. 12 (a) ͑4͉͒ 6 Ϫ 7 ͉ (b) 5͉͞ Ϫ2 ͉ (c) ͉ Ϫ1 ͉ ϩ ͉ Ϫ9 ͉ (b) y is nonnegative. 7 Ϫ 23 ͉ (c) ͉ 51 Ϫ 13 ͉ Exer. 15 – 18: The given numbers are coordinates of points A, B, and C, respectively, on a coordinate line. Find the distance. (a) d(A, B) (b) d(B, C ) (c) d(C, B) (d) d(A, C ) 15 3, 7, Ϫ5 16 Ϫ6, Ϫ2, 4 17 Ϫ9, 1, 10 18 8, Ϫ4, Ϫ1 Exer. 41–42: Approximate the real-number expression to four decimal places. 64 (b) ␲ 3 Exer.

Polynomials Example Leading coefficient Degree 3x 4 ϩ 5x 3 ϩ ͑Ϫ7͒x ϩ 4 x 8 ϩ 9x 2 ϩ ͑Ϫ2͒x Ϫ5x2 ϩ 1 7x ϩ 2 8 3 1 Ϫ5 7 8 4 8 2 1 0 By definition, two polynomials are equal if and only if they have the same degree and the coefficients of like powers of x are equal. If all the coefficients of a polynomial are zero, it is called the zero polynomial and is denoted by 0. However, by convention, the degree of the zero polynomial is not zero but, instead, is undefined. If c is a nonzero real number, then c is a polynomial of degree 0.

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