By Earl W. Swokowski, Jeffery A. Cole
Transparent motives, an uncluttered and attractive format, and examples and routines that includes various real-life purposes have made this article well known between scholars 12 months after yr. This most recent variation of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY keeps those positive aspects. the issues were continually praised for being at simply the appropriate point for precalculus scholars such as you. The booklet additionally presents calculator examples, together with particular keystrokes that make it easier to use quite a few graphing calculators to resolve difficulties extra quick. probably such a lot important-this ebook successfully prepares you for additional classes in arithmetic.
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Additional resources for Algebra and Trigonometry with Analytic Geometry
The coefficient ak of the highest power of x is called the leading coefficient of the polynomial. The following chart contains specific illustrations of polynomials. Polynomials Example Leading coefficient Degree 3x ϩ 5x 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 4 3 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.
Definition of Absolute Value (1) If a Ն 0, then ͉ a ͉ ϭ a. (2) If a Ͻ 0, then ͉ a ͉ ϭ Ϫa. Since a is negative in part (2) of the definition, Ϫa represents a positive real number. Some special cases of this definition are given in the following illustration. ILLUS TRATION The Absolute Value Notation ͉ a ͉ ͉ 3 ͉ ϭ 3, since 3 Ͼ 0. ͉Ϫ3͉ ϭ Ϫ͑Ϫ3͒, since Ϫ3 Ͻ 0. Thus, ͉ Ϫ3 ͉ ϭ 3. ͉ 2 Ϫ ͙2 ͉ 2 Ϫ ͙2, since 2 Ϫ ͙2 Ͼ 0. ͉ ͙2 Ϫ 2 ͉ Ϫ͑ ͙2 Ϫ 2 ͒, since ͙2 Ϫ 2 Ͻ 0. Thus, ͉ ͙2 Ϫ 2 ͉ 2 Ϫ ͙2. In the preceding illustration, ͉ 3 ͉ ͉ Ϫ3 ͉ and ͉ 2 Ϫ ͙2 ͉ ͉ ͙2 Ϫ 2 ͉.
The positive direction is noted by placing an arrowhead on l, as shown in Figure 2. The numbers that correspond to points to the right of O in Figure 2 are positive real numbers. Numbers that correspond to points to the left of O are negative real numbers. The real number 0 is neither positive nor negative. Note the difference between a negative real number and the negative of a real number. In particular, the negative of a real number a can be positive. For example, if a is negative, say a ϭ Ϫ3, then the negative of a is Ϫa ϭ Ϫ͑Ϫ3͒ ϭ 3, which is positive.