By Ron Larson
This market-leading textual content maintains to supply scholars and teachers with sound, always based reasons of the mathematical suggestions. Designed for a one-term direction that prepares scholars for additional research in arithmetic, the hot 8th version keeps the positive aspects that experience regularly made university Algebra an entire resolution for either scholars and teachers: attention-grabbing functions, pedagogically potent layout, and leading edge expertise mixed with an abundance of conscientiously constructed examples and exercises.
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Worthwhile illustrations and workouts integrated all through this lucid assurance of team idea, Galois idea and classical excellent conception stressing facts of significant theorems. contains many historic notes. Mathematical facts is emphasised. contains 24 tables and figures. Reprint of the 1971 version.
This market-leading textual content keeps to supply scholars and teachers with sound, continually based causes of the mathematical strategies. Designed for a one-term direction that prepares scholars for extra learn in arithmetic, the hot 8th variation keeps the good points that experience continuously made collage Algebra a whole resolution for either scholars and teachers: fascinating purposes, pedagogically potent layout, and leading edge know-how mixed with an abundance of rigorously built examples and routines.
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Extra resources for College Algebra (8th Edition)
C. 5 5 ϭ because Ί125 64 4 4 3 3 ϭ 53 125 ϭ . 43 64 5 Ϫ32 ϭ Ϫ2 because ͑Ϫ2͒5 ϭ Ϫ32. d. Ί 4 Ϫ81 is not a real number because there is no real number that can be raised to the e. Ί fourth power to produce Ϫ81. Now try Exercise 65. 20 Chapter P Prerequisites Here are some generalizations about the nth roots of real numbers. Generalizations About nth Roots of Real Numbers Real Number a Integer n Root(s) of a Example a > 0 n > 0, n is even. n a, n a Ί ϪΊ 4 81 ϭ 3, 4 81 ϭ Ϫ3 Ί ϪΊ a > 0 or a < 0 n is odd.
The domain of the expression xϩ2 xϪ3 is the set of all real numbers except x ϭ 3, which would result in division by zero, which is undefined. Now try Exercise 7. The quotient of two algebraic expressions is a fractional expression. Moreover, the quotient of two polynomials such as 1 , x 2x Ϫ 1 , xϩ1 or x2 Ϫ 1 x2 ϩ 1 is a rational expression. Simplifying Rational Expressions Recall that a fraction is in simplest form if its numerator and denominator have no factors in common aside from ± 1. To write a fraction in simplest form, divide out common factors.
Use that list to determine whether Ί5233 is an integer. 129. THINK ABOUT IT Square the real number 5͞Ί3 and note that the radical is eliminated from the denominator. Is this equivalent to rationalizing the denominator? Why or why not? 130. CAPSTONE (a) Explain how to simplify the expression ͑3x3 yϪ2͒Ϫ2. (b) Is the expression or why not? Ίx4 in simplest form? 3 POLYNOMIALS AND SPECIAL PRODUCTS What you should learn Polynomials • Write polynomials in standard form. • Add, subtract, and multiply polynomials.