By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Those authors have created a publication to actually aid scholars visualize arithmetic for greater comprehension. via growing algebraic visible side-by-sides to resolve a variety of difficulties within the examples, the authors express scholars the connection of the algebraic answer with the visible, frequently graphical, resolution. moreover, the authors have further various new instruments to aid scholars greater use the publication for max effectiveness not to in basic terms move the direction, yet really comprehend the material.
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Additional resources for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
X ϩ 1͒ ͑x Ϫ 2͒ ͑3x Ϫ 8͒ Ϫ2x Ϫ h 2 2 73. x 3 ϩ 2x 2 ϩ 11x ϩ 20 2͑x ϩ 1͒ ͑2 ϩ x͒ 74. 6 39 • Radical Notation and Rational Exponents nth Root A number c is said to be an nth root of a if c n a. The symbol ͙a denotes the nonnegative square root of a, and the symn 3 bol ͙ a denotes the real-number cube root of a. The symbol ͙ a denotes n the nth root of a, that is, a number whose nth power is a. The symbol ͙ is called a radical, and the expression under the radical is called the radicand. The number n (which is omitted when it is 2) is called the index.
N͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ ͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ ϩ 2и3и4 2и3 73. x 2 Ϫ 9 5x 2 Ϫ 15x ϩ 45 x 2 ϩ x и ϩ x 3 ϩ 27 x 2 Ϫ 2x Ϫ 3 4 ϩ 2x ͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ 3͑x Ϫ 1͒2͑x ϩ 2͒ x 2 ϩ 2x Ϫ 3 x2 Ϫ 1 2x ϩ 1 71. 74. Ϭ Ϫ 2 2и3 ͑x Ϫ 3͒ ͑x ϩ 3͒ ͑Ϫx ϩ 10͒ x Ϫ x Ϫ 12 x 2 Ϫ 16 x 2 ϩ 2x ϩ 1 ͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ ͑n ϩ 4͒ 72. ͑2x Ϫ 13͒ ͑x Ϫ 5͒ ͑x ϩ 2͒ 2и3и4 58. x 2 ϩ 3x ϩ 3 x 3 ϩ 2x 2 ϩ 11x ϩ 20 ͑x ϩ 1͒ ͑x Ϫ 2͒ ͑3x Ϫ 8͒ 74. 73. ͑x ϩ 1͒2 Ϫ2x Ϫ h 2͑x ϩ 1͒ ͑2 ϩ x͒ 68. 2 x ͑x ϩ h͒2 57. 6 Radical Notation and Rational Exponents Simplify radical expressions.
1 ϩ 1 1ϩ 5x ϩ 3 3x ϩ 2 1 1ϩ 1ϩ 1 x Perform the indicated operations and, if possible, simplify. n͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 1͒ ͑n ϩ 2͒ 71. ϩ 2и3 2 72. n͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ ͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ ϩ 2и3и4 2и3 73. x 2 Ϫ 9 5x 2 Ϫ 15x ϩ 45 x 2 ϩ x и ϩ x 3 ϩ 27 x 2 Ϫ 2x Ϫ 3 4 ϩ 2x ͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ 3͑x Ϫ 1͒2͑x ϩ 2͒ x 2 ϩ 2x Ϫ 3 x2 Ϫ 1 2x ϩ 1 71. 74. Ϭ Ϫ 2 2и3 ͑x Ϫ 3͒ ͑x ϩ 3͒ ͑Ϫx ϩ 10͒ x Ϫ x Ϫ 12 x 2 Ϫ 16 x 2 ϩ 2x ϩ 1 ͑n ϩ 1͒ ͑n ϩ 2͒ ͑n ϩ 3͒ ͑n ϩ 4͒ 72. ͑2x Ϫ 13͒ ͑x Ϫ 5͒ ͑x ϩ 2͒ 2и3и4 58. x 2 ϩ 3x ϩ 3 x 3 ϩ 2x 2 ϩ 11x ϩ 20 ͑x ϩ 1͒ ͑x Ϫ 2͒ ͑3x Ϫ 8͒ 74.