§ 2. Òåîðèÿ äåëèìîñòè ìíîãî÷ëåíîâ
- ¹ 21. Íàéäèòå íàèáîëüøèé îáùèé äåëèòåëü ìíîãî÷ëåíà
- f(x) è åãî
ïðîèçâîäíîé f ¢(x).
21.01. f(x) =
(õ + 2)2 (õ4 – 16) (õ3 – 8);
21.02. f(x) =
(õ – 1) (õ4 – 1) (õ3 + 1);
21.03. f(x) =
(õ – 2)2 (õ4 – 16) (õ3 + 8);
21.04. f(x) =
(õ – 1)2 (õ2 – 1) (õ3 + 1) (õ + 1)2;
21.05. f(x) =
(õ2 – 4) (õ4 – 16) (õ + 2)2 (õ – 2);
21.06. f(x) =
(õ2 – õ – 2) (õ2 – 1) (õ2 – 4) (õ3 + 8);
21.07. f(x) =
(õ2 + õ – 2) × (õ – 1)2 × (õ3 + 1);
21.08. f(x) =
(õ + 3)2 × (õ4 – 81) × (õ3 – 27);
21.09. f(x) =
(õ – 3)2 × (õ4 – 81) × (õ3 + 27);
21.10. f(x) =
(õ2 + 5õ + 6) × (õ2 – 9) × (õ + 3)2;
21.11. f(x) =
(õ2 – 5õ + 6) × (õ2 – 9) × (õ – 3)2 × (õ – 2);
21.12. f(x) =
(õ2 – õ – 6) × (õ2 – 9) × (õ2 – 4);
21.13. f(x) =
(õ2 + õ – 6) × (õ2 – 9) × (õ2 – 4) × (õ + 3);
21.14. f(x) =
(õ + 4)2 × (õ2 – 16) × (õ3 – 64);
21.15. f(x) =
(õ – 4)2
× (õ2 – 16) × (õ3 + 64);
21.16. f(x) =
(õ2 + 4õ + 3) × (õ2 – 1) × (õ2 – 9) × (õ + 1)2;
21.17. f(x) =
(õ2 – 4õ + 3) × (õ2 – 1) × (õ2 – 9);
21.18. f(x) =
(õ2 – 1) × (õ2 – 9) × (õ – 1)2 × (õ + 3)2;
21.19. f(x) =
(õ3 – 27) × (õ2 – 9) × (õ + 3)2;
21.20. f(x) =
(õ3 + 27) × (õ2 – 9) × (õ – 3)2;
21.21. f(x) =
(õ2 – õ – 20) × (õ2 – 25) × (õ2 – 16);
21.22. f(x) =
(õ2 – õ – 20) × (õ3 – 125) × (õ2 – 16) × (x + 4);
21.23. f(x) =
(õ3 – 125) × (õ – 5)2 × (x + 5)2 (x2 – 25);
21.24. f(x) =
(õ2 – 16) × (õ3 – 64) × (õ + 4)2 × (õ – 4);
21.25. f(x) =
(õ2 – 9) × (õ – 3)2 × (õ + 3)2 × (õ2 – 4x + 3);
21.26. f(x) =
(õ2 – 9) × (õ + 3)2 × (õ – 3)2 × (õ2 – 4x + 3);
21.27. f(x) =
(õ – 8) × (õ2 + 4x + 4) × (õ2 – x – 2) × (õ2 – 1);
21.28. f(x) =
(õ – 2)2 × (õ + 2)2 × (õ3– 8) × (õ3 + x – 2);
21.29. f(x) =
(õ3 – 125) × (õ2 – 25) × (õ2 + 10x + 25) × (õ2 + 5x + 25);
21.30. f(x) =
(õ3 + 125) × (õ2 – 10x + 25) × (õ2 – 5x + 25) × (x + 5);
21.31. f(x) =
(õ2 – 36) × (õ3 – 216) × (õ2 + 6x + 36);
21.32. f(x) =
(õ2 – 36) × (õ2 – 12x + 36) × (õ3 – 216);
21.33. f(x) =
(õ2 + 7õ + 6) × (õ2 – 1) × (õ2 – 36);
21.34. f(x) =
(õ2 – 7x + 6) × (õ2 – 1) × (õ2 – 2x + 1);
21.35. f(x) =
(õ2 – 1) × (õ2 + 2x + 1) × (õ2 – 4x + 3);
21.36. f(x) =
(õ2 – x – 12) × (õ2 – 4) × (õ2 – 9).