§ 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)24 – 16) (õ3 – 8); 

21.02. f(x) = (õ – 1) (õ4 – 1) (õ3 + 1);

21.03. f(x) = (õ – 2)24 – 16) (õ3 + 8);

21.04. f(x) = (õ – 1)22 – 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) ×2 – 9).

 

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