By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Those authors have created a booklet to truly aid scholars visualize arithmetic for larger comprehension. by means of developing algebraic visible side-by-sides to resolve a number of difficulties within the examples, the authors exhibit scholars the connection of the algebraic answer with the visible, frequently graphical, resolution. additionally, the authors have additional various new instruments to assist scholars greater use the booklet for max effectiveness not to in simple terms go the direction, yet really comprehend the material.
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Additional resources for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
A rational expression is the quotient of two polynomials. For example, 3 , 5 2 , xϪ3 and x2 Ϫ 4 x Ϫ 4x Ϫ 5 2 are rational expressions. , publishing as Pearson Addison-Wesley 99. 3͑z Ϫ 2͒ ͑z 2 ϩ 2z ϩ 4͒ 100. 4͑t ϩ 3͒ ͑t 2 Ϫ 3t ϩ 9͒ 101. 2ab͑2a2 ϩ 3b 2 ͒ ͑4a4 Ϫ 6a2b 2 ϩ 9b 4 ͒ 102. 3a2x͑2x Ϫ 5a2 ͒ ͑4x 2 ϩ 10a2x ϩ 25a4 ͒ 116. a͑5 Ϫ 2a͒ ͑25 ϩ 10a ϩ 4a 2 ͒ 128. 5 • Rational Expressions 31 The Domain of a Rational Expression The domain of an algebraic expression is the set of all real numbers for which the expression is defined.
The factorization is ͑x ϩ 2͒ ͑x ϩ 3͒. We have x 2 ϩ 5x ϩ 6 ͑x ϩ 2͒ ͑x ϩ 3͒. We can check this by multiplying: ͑x ϩ 2͒ ͑x ϩ 3͒ x 2 ϩ 3x ϩ 2x ϩ 6 x 2 ϩ 5x ϩ 6. EXAMPLE 4 Factor: 2y 2 Ϫ 14y ϩ 24. Solution First, we look for a common factor. Each term has a factor of 2, so we factor it out first: 2y 2 Ϫ 14y ϩ 24 2͑ y 2 Ϫ 7y ϩ 12͒. Now we consider the trinomial y 2 Ϫ 7y ϩ 12. We look for two numbers whose product is 12 and whose sum is Ϫ7. Since the constant term, 12, is positive and the coefficient of the middle term, Ϫ7, is negative, we look for a factorization of 12 in which both factors are negative.
180 5 16. ͙250 3 3 19. ͙128c 2d 4 18. ͙ 135 8͙2 ͉ c ͉ d 2 4 45 3 6 m12n24 64 m2n4 2 ͙ 40m 2 3 ͙ 5m 3 3 3͙ 5 4 2 4 3͉ m ͉n ͙ mn2 23. ͙x 2 Ϫ 4x ϩ 4 ͉x Ϫ 2͉ 24. ͙x 2 ϩ 16x ϩ 64 Simplify. Assume that no radicands were formed by raising negative quantities to even powers. 25. ͙10 ͙30 10͙3 26. ͙28 ͙14 14͙2 ͙ 3x 2 39. 3 ͙ 24x 5 ͱ ͱ 41. 43. 3 5 3 2͑x ϩ 4͙͒ ͑x ϩ 4͒2 3 ͱ 5͙10 21. ͙ 48x 6y 4 2͉ x ͉ ͉ y ͉͙ 3x 2 22. ͙ 243m5n 10 5 32. ͙ 8x 3y 4 ͙ 4x 4y 34. ͙ 4͑x ϩ 1͒2 ͙ 18͑x ϩ 1͒2 35. 5͙21 30. ͙3y 4z ͙20z 33.