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

By Earl Swokowski, Jeffery A. Cole

ISBN-10: 0495559717

ISBN-13: 9780495559719

The most recent 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 apparent, the time-tested workout units function numerous purposes, its uncluttered structure is attractive, 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 additional classes in arithmetic via its first-class, time-tested challenge units.

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

Sample text

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. 43–44: Approximate the real-number expression. Express the answer in scientific notation accurate to four significant figures. 52 ϫ 10 3 Exer. 19–24: The two given numbers are coordinates of points A and B, respectively, on a coordinate line.

We may also consider polynomials in variables other than x. For example, Ϫ 3z7 ϩ 8 Ϫ 2 5 z 4 is a polynomial in z of degree 7. We often arrange the terms of a polynomial in order of decreasing powers of the variable; thus, we write 2 2 5z 2 2 5z Ϫ 3z7 ϩ 8 Ϫ 25 z 4 ϭ Ϫ3z7 Ϫ 25 z4 ϩ 25 z2 ϩ 8. We may regard a polynomial in x as an algebraic expression obtained by employing a finite number of additions, subtractions, and multiplications involving x. If an algebraic expression contains divisions or roots involving a variable x, then it is not a polynomial in x.

By trial and error, we obtain the factorization 4x 4y Ϫ 11x 3y 2 ϩ 6x 2y 3 ϭ x 2y͑4x Ϫ 3y͒͑x Ϫ 2y͒. L If a sum contains four or more terms, it may be possible to group the terms in a suitable manner and then find a factorization by using distributive properties. This technique, called factoring by grouping, is illustrated in the next example. 38 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA EXAMPLE 10 Factoring by grouping Factor: (a) 4ac ϩ 2bc Ϫ 2ad Ϫ bd (b) 3x 3 ϩ 2x 2 Ϫ 12x Ϫ 8 (c) x 2 Ϫ 16y 2 ϩ 10x ϩ 25 SOLUTION (a) We group the first two terms and the last two terms and then proceed as follows: 4ac ϩ 2bc Ϫ 2ad Ϫ bd ϭ ͑4ac ϩ 2bc͒ Ϫ ͑2ad ϩ bd͒ ϭ 2c͑2a ϩ b͒ Ϫ d͑2a ϩ b͒ At this stage we have not factored the given expression because the right-hand side has the form 2ck Ϫ dk with k ϭ 2a ϩ b.

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


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