By Revathi Narasimhan
In response to years of expertise educating and writing supplemental fabrics for extra conventional precalculus texts, Reva Narasimhan takes a functions-focused method of educating and studying algebra and trigonometry recommendations. This new sequence builds up correct options utilizing capabilities as a unifying topic, repeating and increasing on connections to simple capabilities. Visualization and research inspire the functions-based process, permitting scholars to higher hold the cloth to be used in later calculus classes.
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Extra info for College Algebra and Trigonometry: Building Concepts and Connections
A ᭤A 3 5 polynomial with three terms, such as 4t 6 Ϫ t 2 Ϫ ͙3, is called a trinomial. 4 Addition and Subtraction of Polynomials Terms of an expression that have the same variable raised to the same power are called like terms. 4 ■ Polynomials 29 their respective coefficients using the distributive property. This is illustrated in the following example. 2 Adding and Subtracting Polynomials Example Add or subtract each of the following. (a) (3x 3 ϩ 2x 2 Ϫ 5x ϩ 7) ϩ (x 3 Ϫ x 2 ϩ 5x Ϫ 2) ͩ ͪ 3 2 s Ϫ (s4 Ϫ s2) 4 (b) s4 ϩ ᭤Solution (a) Rearranging terms so that the terms with the same power are grouped together gives (3x 3 ϩ 2x 2 Ϫ 5x ϩ 7) ϩ (x 3 Ϫ x 2 ϩ 5x Ϫ 2) (3x 3 ϩ x 3) ϩ (2x 2 Ϫ x 2) ϩ (Ϫ5x ϩ 5x) ϩ (7 Ϫ 2).
2y ϩ 1)2 15. (Ϫ9x 3 ϩ 6x 2 Ϫ 20x ϩ 3) ϩ (x 2 Ϫ 5x Ϫ 6) 55. (6 Ϫ 5t)2 56. (Ϫ9 ϩ 2u)2 16. (5t 3 ϩ 16t Ϫ 12) Ϫ (2t 3 Ϫ 4t 2 ϩ t) ϩ (Ϫ5t 2 Ϫ 3t ϩ 7) 57. (v ϩ 9)(v Ϫ 9) 58. (z Ϫ 7)(z ϩ 7) 17. (3x 4 Ϫ x 3 ϩ x 4 Ϫ 4) ϩ (x 5 ϩ 7x 3 Ϫ 3x 2 ϩ 5) 59. (9s ϩ 7)(7 Ϫ 9s) 60. (Ϫ6 ϩ 5t)(Ϫ5t Ϫ 6) 18. (z 5 Ϫ 4z 4 ϩ 7) Ϫ (Ϫz 3 ϩ 15z 2 Ϫ 8z) 61. (v 2 ϩ 3)(v 2 Ϫ 3) 62. (7 Ϫ z 2)(7 ϩ z 2) 19. (x 5 Ϫ 3x 4 ϩ 7x) Ϫ (4x 5 Ϫ 3x 3 ϩ 8x ϩ 1) 63. (5y 2 Ϫ 4)(5y 2 ϩ 4) 64. (2x 2 ϩ 3)(2x 2 Ϫ 3) 20. (3v 4 Ϫ 6v ϩ 5) ϩ (25v 3 Ϫ 16v 3 ϩ 3v 2) 65.
Example 7 Calculator Use and Order of Operations Evaluate the following expressions on your calculator. Check the calculator output against a hand calculation. (a) 4 ϩ 10 Ϭ 5 ϩ 2 4 ϩ 10 (b) 5ϩ2 ᭤Solution (a) Enter 4 ϩ 10 Ϭ 5 ϩ 2 in the calculator as 4 ϩ 10 Ϭ 5 ϩ 2. The result is 8. This result checks with a hand calculation of 4 ϩ 10 Ϭ 5 ϩ 2 4 ϩ 2 ϩ 2 8. 1 ■ The Real Number System 9 (b) To calculate 4 ϩ 10 , 5ϩ2 we need to proceed with caution. The additions in the numer- ator and denominator must be performed first, before the division.
College Algebra and Trigonometry: Building Concepts and Connections by Revathi Narasimhan