Read e-book online Algebra and Trigonometry with Analytic Geometry, Classic PDF

By Earl Swokowski, Jeffery A. Cole

ISBN-10: 0495559717

ISBN-13: 9780495559719

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 characteristic a number of functions, its uncluttered format 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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Additional resources for Algebra and Trigonometry with Analytic Geometry, Classic Edition

Example text

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. Such polynomials (together with the zero polynomial) are constant polynomials. If a coefficient of a polynomial is negative, we usually use a minus sign between appropriate terms. To illustrate, 3x 2 ϩ ͑Ϫ5͒x ϩ ͑Ϫ7͒ ϭ 3x 2 Ϫ 5x Ϫ 7. 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.

To factor a polynomial means to express it as a product of irreducible polynomials. The greatest common factor (gcf ) of an expression is the product of the factors that appear in each term, with each of these factors raised to the smallest nonzero exponent appearing in any term. In factoring polynomials, it is advisable to first factor out the gcf, as shown in the following illustration. ILLUS TRATION Factored Polynomials 8x 2 ϩ 4xy ϭ 4x͑2x ϩ y͒ 25x 2 ϩ 25x Ϫ 150 ϭ 25͑x 2 ϩ x Ϫ 6͒ ϭ 25͑x ϩ 3͒͑x Ϫ 2͒ 4x 5y Ϫ 9x 3y 3 ϭ x 3y͑4x 2 Ϫ 9y 2͒ ϭ x 3y͑2x ϩ 3y͒͑2x Ϫ 3y͒ It is usually difficult to factor polynomials of degree greater than 2.

Every polynomial ax ϩ b of degree 1 is irreducible. Before we factor a polynomial, we must specify the number system (or set) from which the coefficients of the factors are to be chosen. In this chapter we shall use the rule that if a polynomial has integral coefficients, then the factors should be polynomials with integral coefficients. To factor a polynomial means to express it as a product of irreducible polynomials. The greatest common factor (gcf ) of an expression is the product of the factors that appear in each term, with each of these factors raised to the smallest nonzero exponent appearing in any term.

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


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