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appendix_b_page_530

# appendix_b_page_530 - 11:58 l24-appb-sv Sheet number 1 Page...

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January 27, 2005 11:58 l24-appb-sv Sheet number 1 Page number 530 black 530 APPENDIX B Solving Polynomial Equations EXERCISE SET B 1. (a) q ( x ) = x 2 + 4 x + 2 , r ( x ) = 11 x + 6 (b) q ( x ) = 2 x 2 + 4 , r ( x ) = 9 (c) q ( x ) = x 3 x 2 + 2 x 2 , r ( x ) = 2 x + 1 2. (a) q ( x ) = 2 x 2 x + 2 , r ( x ) = 5 x + 5 (b) q ( x ) = x 3 + 3 x 2 x + 2 , r ( x ) = 3 x 1 (c) q ( x ) = 5 x 3 5 , r ( x ) = 4 x 2 + 10 3. (a) q ( x ) = 3 x 2 + 6 x + 8 , r ( x ) = 15 (b) q ( x ) = x 3 5 x 2 + 20 x 100 , r ( x ) = 504 (c) q ( x ) = x 4 + x 3 + x 2 + x + 1 , r ( x ) = 0 4. (a) q ( x ) = 2 x 2 + x 1 , r ( x ) = 0 (b) q ( x ) = 2 x 3 5 x 2 + 3 x 39 , r ( x ) = 147 (c) q ( x ) = x 6 + x 5 + x 4 + x 3 + x 2 + x + 1 , r ( x ) = 2 5. x 0 1 3 7 p ( x ) 4 3 101 5001 6. x 1 1 3 3 7 7 21 21 p ( x ) 24 12 12 0 420 168 10416 7812 7. (a) q ( x ) = x 2 + 6 x + 13 , r = 20 (b) q ( x ) = x 2 + 3 x 2 , r = 4 8. (a) q ( x ) = x 4 x 3 + x 2 x + 1 , r = 2 (b) q ( x ) = x 4 + x 3 + x 2 + x + 1 , r = 0 9. Assume r = a/b a and b integers with a > 0: (a) b divides 1, b = ± 1; a divides 24, a = 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24; the possible candidates are 1 , ± 2 , ± 3 , ± 4 , ± 6 , ± 8 , ± 12 , ± 24 } (b) b divides 3 so b = ± 1 , ± 3; a divides 10 so a = 1 , 2 , 5 , 10; the possible candidates are 1 , ± 2 , ± 5 , ± 10 , ± 1 / 3 , ± 2 /

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