Ruffini

Factoritza els polinomis fent servir la regla de Ruffini.

Exercicis 1–25

1. \(x^3 + 8x^2 + 15x\) =
2. \(x^3 - 7x^2 + 16x - 12\) =
3. \(x^3 + 3x^2 - 10x\) =
4. \(2x^3 - 8x^2 + 2x + 12\) =
5. \(x^4 - 5x^2 + 4\) =
6. \(x^4 - x^3 - x^2 + x\) =
7. \(x^4 - 3x^3 - 13x^2 + 38x - 24\) =
8. \(x^5 - 5x^4 + 7x^3 - 3x^2\) =
9. \(x^4 + 3x^3 + 4x^2 + 6x + 4\) =
10. \(3x^3 + 3x^2 - 18x\) =
11. \(x^4 - 3x^3 + 3x^2 - 3x + 2\) =
12. \(2x^3 - 2x^2 - 12x\) =
13. \(x^4 - x^3 - 7x^2 + x + 6\) =
14. \(4x^4 - 6x^3 + 2\) =
15. \(x^3 - 2x^2 - x - 2\) =
16. \(x^3 - 4x^2 + 5x - 2\) =
17. \(x^3 + 2x^2 - 4x - 8\) =
18. \(2x^3 + 4x^2 - 10x - 12\) =
19. \(x^3 - 3x^2 - x + 3\) =
20. \(x^3 - 5x^2 + 8x - 4\) =
21. \(x^3 + 3x^2 - 4\) =
22. \(2x^3 - x^2 - 25x - 12\) =
23. \(x^3 - 5x^2 + 7x - 3\) =
24. \(x^3 - 2x^2 - 4x + 8\) =
25. \(x^3 + 4x^2 - x - 4\) =

Solucions

1. \(x(x+3)(x+5)\)
2. \((x-2)^2(x-3)\)
3. \(x(x-2)(x+5)\)
4. \(2(x+1)(x-2)(x-3)\)
5. \((x-1)(x+1)(x-2)(x+2)\)
6. \(x(x-1)^2(x+1)\)
7. \((x-1)(x-2)(x-3)(x+4)\)
8. \(x^2(x-1)^2(x-3)\)
9. \((x^2+2)(x+2)(x+1)\)
10. \(3x(x-2)(x+3)\)
11. \((x-1)(x-2)(x^2+1)\)
12. \(2x(x+2)(x-3)\)
13. \((x+2)(x-1)(x+1)(x-3)\)
14. \(2(x-1)(2x^3-x^2-x-1)\)
15. \((x+1)(x-1)(x-2)\)
16. \((x-1)^2(x-2)\)
17. \((x+2)^2(x-2)\)
18. \(2(x+1)(x-2)(x+3)\)
19. \((x-3)(x-1)(x+1)\)
20. \((x-2)^2(x-1)\)
21. \((x+2)^2(x-1)\)
22. \((x+3)(x-4)(2x+1)\)
23. \((x-1)^2(x-3)\)
24. \((x-2)^2(x+2)\)
25. \((x+4)(x-1)(x+1)\)

Exercicis 26–51

26. \(3x^3 + 6x^2 - 45x - 108\) =
27. \(9x^2 - 25\) =
28. \(36x^6 - 49x^4\) =
29. \(121 - 25x^8\) =
30. \(3x^4 + 6x^3 + 6x^2 + 6x + 3\) =
31. \(x^4 + 3x^3 + 4x^2 + 6x + 4\) =
32. \(3x^2 + 14x - 5\) =
33. \(x^3 + 5x^2 + 8x\) =
34. \(4x^5 + 2x^4 - 2x^3\) =
35. \(2x^3 - 10x^2 + 14x - 6\) =
36. \(3x^4 - 2x^3 - 13x^2 + 8x + 4\) =
37. \(x^4 - 4x^3 - 6x^2 + 36x - 27\) =
38. \(x^4 + 3x^3 - 2x^2 - 12x + 9\) =
39. \(7x^4 + 28x^3 + 21x^2 - 28x - 28\) =
40. \(x^4 - 13x^3 + 27x^2 - 23x + 7\) =
41. \(4x^3 + 3x^2 - x - 3\) =
42. \(2x^4 - 2x^3 - 22x^2 + 10x + 60\) =
43. \(4x^4 - 28x^2 + 49\) =
44. \(4x^4 + 12x^3 + 26x^2 + 24x + 8\) =
45. \(x^6 - 14x^4 + 49x^2 - 36\) =
46. \(x^4 + 6x^3 + 9x^2 - 4x - 12\) =
47. \(x^4 + 10x^3 + 37x^2 + 60x + 36\) =
48. \(x^5 - 2x^3 + x\) =
49. \(x^6 + 2x^5 - 3x^4 - 4x^3 + 4x^2\) =
50. \(x^4 + 3x^3 - 3x^2 - 11x - 6\) =
51. \(10x^4 - 60x^2 + 90\) =

Solucions

26. \(3(x-4)(x+3)^2\)
27. \((3x+5)(3x-5)\)
28. \(x^4(6x-7)(6x+7)\)
29. \((11-5x^4)(11+5x^4)\)
30. \(3(x+1)^2(x^2+1)\)
31. \((x+1)(x+2)(x^2+2)\)
32. \((3x-1)(x+5)\)
33. \(x(x^2+5x+8)\)
34. \(2x^3(2x-1)(x+1)\)
35. \(2(x-1)^2(x-3)\)
36. \((3x+1)(x+2)(x-2)(x-1)\)
37. \((x-3)^2(x+3)(x-1)\)
38. \((x+3)^2(x-1)^2\)
39. \(7(x+1)(x-1)(x-2)^2\)
40. \((x-1)^3(2x-7)\)
41. \(x(x+1)^2(2x-1)\)
42. \((x+2)(x-3)\,(x-\sqrt{5})\,(x+\sqrt{5})\)
43. \((2x^2-7)^2\)
44. \(2(x+1)^2(x+2)^2\)
45. \((x-1)(x-2)(x-3)(x+1)(x+2)(x+3)\)
46. \((x-1)(x+2)^2(x+3)\)
47. \((x+3)^2(x+2)^2\)
48. \(x(x+1)^2(x-1)^2\)
49. \(x^2(x-1)^2(x+2)^2\)
50. \((x+1)^2(x-2)(x+3)\)
51. \(10\,(x-\sqrt{3})^2\,(x+\sqrt{3})^2\)