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(Answers for Chapter 2: Polynomial and Rational Functions) A.2.1 CHAPTER 2: Polynomial and Rational Functions SECTION 2.1: QUADRATIC FUNCTIONS (AND PARABOLAS) 1) a) Upward; b) 1, ± 9 () ; c) x = 1 d) ± 8 , or 0, ± 8 e) ± 2 and 4, or ± 2, 0 and 4, 0 f) 2, ± 8 g) 2) a) Downward; b) ± 11 4 , 243 8 ² ³ ´ µ · , or ± 2.75, 30.375 ; c) x = ± 11 4 , or x = ± 2.75 d) ± 15 , or 0, ± 15 e) ± 5 and ± 1 2 , or ± 5, 0 and ± 1 2 ,0 ² ³ ´ µ ·

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(Answers for Chapter 2: Polynomial and Rational Functions) A.2.2 3) a) Upward; b) 2, 3 () ; c) x = 2 d) 7, or 0, 7 e) None 4) a) y = x + 4 2 ± 6 ; b) Upward; c) ± 4, ± 6 5) a) y = ± 4 x ± 3 2 ± 1 ; b) Downward; c) 3, ± 1 6) a) y = 2 x ± 7 2 ² ³ ´ µ · 2 + 5 2 , or y = 2 x ± 3.5 2 + 2.5 b) Upward c) 7 2 , 5 2 ± ² ³ ´ µ , or 3.5, 2.5 7) y = ± 2 9 x ± 6 2 ± 3 , or y = ± 2 9 x 2 + 8 3 x ± 11 8) a) ± \$2000 (i.e., a net loss of \$2000) b) 7 widgets c) \$450 d) 4 widgets and 10 widgets 9) a) 384 feet b) 5 2 seconds, or 2.5 seconds c) 484 feet d) 8 seconds
(Answers for Chapter 2: Polynomial and Rational Functions) A.2.3 SECTION 2.2: POLYNOMIAL FUNCTIONS OF HIGHER DEGREE 1) a) ± , ±² b) ± , ± c) , d) , ± 2) 3 or 1 3) 6, 4, 2, or 0 4) The degree of f is odd and is at least 5. The leading coefficient of fx () is positive. 5) 0, 1, 2, 3, or 4 6) If a is any nonzero real number, we can use anything of the form: ax 2 x + 3 x ± 5 , or ax x + 3 2 x ± 5 , or ax x + 3 x ± 5 2 . 7) If a is any nonzero real number, we can use anything of the form: ax + 2 2 x ± 4 3 . 8) f is a polynomial function, so it is continuous on 1, 2 [] . f 1 () = ± 1 , so f 1 () < 0 . f 2 1 , so f 2 () > 0 . Therefore, by the Intermediate Value Theorem, f has a zero between 1 and 2. 9) a) b) f ± 4 > 0 , f 0 0 , f 3 0 , and f 6 0

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(Answers for Chapter 2: Polynomial and Rational Functions) A.2.4 SECTION 2.3: LONG AND SYNTHETIC POLYNOMIAL DIVISION 1) 3 x ± 5 + 4 x ± 1 2 x 2 + 4 x + 3 2) 4 x + 7 ± 9 x + 2 3 x 2 ± 2 3) ± x 2 + 5 + 3 x 2 ± x + 2 7 x ± x 3 , which some may rewrite as 5 ± x 2 + 3 x 2 ± x + 2 7 x ± x 3 .
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