By Rande P.
Les polynômes permettent de résumer les calculs de base sur les nombres : somme, produit, élévation à une puissance entière. C'est l. a. raison pour laquelle ils se sont si tôt introduits comme outils naturels des mathématiques. Formellement, ils sont utilisés comme des schémas universels pour ces calculs, puisque, par substitution, ils permettent de réaliser tout calcul concret à partir de manipulation abstraite. Dans cet article, nous n'abordons que les propriétés élémentaires de sort algébrique ou arithmétique. Nous nous limiterons aux occasions les plus simples, en particulier en ce qui concerne les polynômes irréductibles et l. a. recherche des racines. Les extensions naturelles de l'étude des polynômes sont los angeles géométrie.
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Evaluate 8 - x 3 + 10 , 5y 2 when x = 4 and y = 6. Answers 9. 84 10. -126 11. -50 12. 120 13. 42 14. -146 15. 96 ft2 16. 64 17. 64 18. 4 Translate each phrase to an algebraic expression. 1. 8 more than b 2. 11 more than t 3. 4 less than c 4. 203 less than d 5. 5 increased by q 6. 18 increased by z 7. b more than a 8. c more than d 9. x divided by y 10. c divided by h 11. x plus w 12. s added to t 13. m subtracted from n 14. p subtracted from q 15. The sum of p and q 16. The sum of a and b 17. Three times q 18.
2. If the signs are the same, then the answer is positive. 3. If the signs are different, then the answer is negative. Do Exercises 39–42. -28 -14 40. 125 , 1-52 41. -75 25 42. 2 , 1-212 Excluding Division by Zero We cannot divide a nonzero number n by zero. By the definition of division, n>0 would be some number that when multiplied by 0 gives n. But when any number is multiplied by 0, the result is 0. Thus the only possibility for n would be 0. Consider 0>0. We might say that it is 5 because 5 # 0 = 0.
1. 4 # 4 # 4 # 4 # 4 2. 6 # 6 # 6 3. 5 # 5 # 5 # 5 # 5 # 5 4. x # x # x # x 5. mmm 6. ttttt 8. 82 7 # 7 # 7 # 7 12 12 12 12 4 4 4 10. a - b a - b a - b 5 5 5 9. 72 Evaluate. 11. 2 7 12. 93 13. 1-225 14. 1-722 1 4 15. a b 3 16. 126 17. 1-423 18. 1-324 19. 622 2 4 20. a b 3 21. 51 22. A 16 B 1 23. 34 0 5 1 24. a b 2 25. A 16 B 0 26. 1-420 7 1 27. a b 8 28. 1-8720 5 -4 32. a b 2 b Rewrite using a positive exponent. Evaluate, if possible. 1 -2 29. a b 4 1 -3 30. a b 5 2 -3 31. a b 3 33. y -5 34. x -6 35.