By Ron Larson
University Algebra with purposes for enterprise and lifestyles Sciences meets the call for for classes that emphasize challenge fixing, modeling, and real-world functions for enterprise and the existence sciences. The authors offer a company beginning in algebraic suggestions and recommended scholars to use their knowing to proper examples and purposes they're more likely to come across in university or of their careers. extra know-how parts to be had via CL MATHSpace improve guide and inspire freshmen. this system addresses the wishes of scholars in any respect levels--and particularly those that could have struggled in prior algebra courses--offering an abundance of examples and routines that make stronger recommendations and make studying extra dynamic. The early advent of services in bankruptcy 1 guarantees compatibility with syllabi and offers a framework for scholar studying. non-compulsory Discovery and Exploration actions are built-in during the textual content; teachers may also choose to use graphing know-how as a device for challenge fixing and evaluation or retention.
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This is called the standard form of a polynomial. Example 1 Rewriting a Polynomial in Standard Form Polynomial Standard Form Degree a. 4x Ϫ 5x Ϫ 2 ϩ 3x Ϫ5x ϩ 4x ϩ 3x Ϫ 2 3 b. 4 Ϫ 9x 2 Ϫ9x 2 ϩ 4 2 c. 8 8͑8 ϭ 8x0͒ 0 2 3 3 2 ✓CHECKPOINT 1 Rewrite the polynomial 7 Ϫ 9x2 ϩ 3x in standard form and state its degree. ■ Polynomials with one, two, and three terms are called monomials, binomials, and trinomials, respectively. 5 Polynomials and Special Products 41 A polynomial that has all zero coefficients is called the zero polynomial, denoted by 0.
32 62. 63. 4 2 Ί 4 ͑3x2͒4 64. Ί 3 x 6 ͑x ϩ 2͒4 66. Ί In Exercises 67–72, simplify the expression. 67. 5Ίx Ϫ 3Ίx 68. 3Ίx ϩ 1 ϩ 10Ίx ϩ 1 69. 5Ί50 ϩ 3Ί8 70. 2Ί27 Ϫ Ί75 71. 2Ί4y Ϫ 2Ί9y 72. 2Ί108 ϩ Ί147 In Exercises 73– 80, use a calculator to approximate the number. ) 3 45 73. Ί 74. Ί57 75. 7 2͞5 76. 1 77. 8 78. 75Ϫ1͞2 3 Ϫ Ί5 2 80. Ϫ4 ϩ Ί12 4 81. Calculator Write the keystrokes you can use to evaluate 4 Ϫ Ί7 in one step on your calculator. 3 82. Calculator Write the keystrokes you can use to evaluate 3 Ί ͑Ϫ5͒5 in one step on your calculator.
Am ϭ amϪn an 3. ͑ab͒m ϭ ambm 4. ab m ϭ am bm 5. ͑am͒n ϭ amn 6. aϪn ϭ 8. ab Ϫn ϭ Product of Powers x7 ϭ x7Ϫ4 ϭ x3 x4 uQotient of Powers ͑5x͒3 ϭ 53x3 ϭ 125x3 Power of a Product 2x Power of a uQotient 3 ϭ 23 8 ϭ 3 x3 x ͑ y3͒Ϫ4 ϭ y3͑Ϫ4͒ ϭ yϪ12 1 an 7. a0 ϭ 1, 32 и 34 ϭ 32ϩ4 ϭ 36 1 y4 yϪ4 ϭ a Definition of negative exponent ͑x2 ϩ 1͒0 ϭ 1 0 ba , Power of a Power 32 n a 0, b 0 Խ Խ ԽԽ Ϫ3 ϭ 23 Definition of zero exponent 3 Խ22Խ ϭ Խ2Խ2 ϭ 22 9. a2 ϭ a 2 ϭ a2 Notice that these properties of exponents apply for all integers m and n, not just positive integers.