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# 6.3E: Ejercicios

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## La práctica hace a la perfección

Factor Trinomios de la Forma $$x^2+bx+c$$

En los siguientes ejercicios, factor cada trinomio de la forma $$x^2+bx+c$$.

1. $$p^2+11p+30$$

Contestar

$$(p+5)(p+6)$$

2. $$w^2+10w+21$$

3. $$n^2+19n+48$$

Contestar

$$(n+3)(n+16)$$

4. $$b^2+14b+48$$

5. $$a^2+25a+100$$

Contestar

$$(a+5)(a+20)$$

6. $$u^2+101u+100$$

7. $$x^2−8x+12$$

Contestar

$$(x−2)(x−6)$$

8. $$q^2−13q+36$$

9. $$y^2−18y+45$$

Contestar

$$(y−3)(y−15)$$

10. $$m^2−13m+30$$

11. $$x^2−8x+7$$

Contestar

$$(x−1)(x−7)$$

12. $$y^2−5y+6$$

13. $$5p−6+p^2$$

Contestar

$$(p−1)(p+6)$$

14. $$6n−7+n^2$$

15. $$8−6x+x^2$$

Contestar

$$(x−4)(x−2)$$

16. $$7x+x^2+6$$

17. $$x^2−12−11x$$

Contestar

$$(x−12)(x+1)$$

18. $$−11−10x+x^2$$

En los siguientes ejercicios, factor cada trinomio de la forma $$x^2+bxy+cy^2$$.

19. $$x^2−2xy−80y^2$$

Contestar

$$(x+8y)(x−10y)$$

20. $$p^2−8pq−65q^2$$

21. $$m^2−64mn−65n^2$$

Contestar

$$(m+n)(m−65n)$$

22. $$p^2−2pq−35q^2$$

23. $$a^2+5ab−24b^2$$

Contestar

$$(a+8b)(a−3b)$$

24. $$r^2+3rs−28s^2$$

25. $$x^2−3xy−14y^2$$

Contestar

Prime

26. $$u^2−8uv−24v^2$$

27. $$m^2−5mn+30n^2$$

Contestar

Prime

28. $$c^2−7cd+18d^2$$

Trinomios Factoriales de la Forma $$ax^2+bx+c$$ Usando Ensayo y Error

En los siguientes ejercicios, factor completamente usando ensayo y error.

29. $$p^3−8p^2−20p$$

Contestar

$$p(p−10)(p+2)$$

30. $$q^3−5q^2−24q$$

31. $$3m^3−21m^2+30m$$

Contestar

$$3m(m−5)(m−2)$$

32. $$11n^3−55n^2+44n$$

33. $$5x^4+10x^3−75x^2$$

Contestar

$$5x^2(x−3)(x+5)$$

34. $$6y^4+12y^3−48y^2$$

35. $$2t^2+7t+5$$

Contestar

$$(2t+5)(t+1)$$

36. $$5y^2+16y+11$$

37. $$11x^2+34x+3$$

Contestar

$$(11x+1)(x+3)$$

38. $$7b^2+50b+7$$

39. $$4w^2−5w+1$$

Contestar

$$(4w−1)(w−1)$$

40. $$5x^2−17x+6$$

41. $$4q^2−7q−2$$

Contestar

$$(4q+1)(q−2)$$

42. $$10y^2−53y−111$$

43. $$6p^2−19pq+10q^2$$

Contestar

$$(2p−5q)(3p−2q)$$

44. $$21m^2−29mn+10n^2$$

45. $$4a^2+17ab−15b^2$$

Contestar

$$(4a−3b)(a+5b)$$

46. $$6u^2+5uv−14v^2$$

47. $$−16x^2−32x−16$$

Contestar

$$−16(x+1)(x+1)$$

48. $$−81a^2+153a+18$$

49. $$−30q^3−140q^2−80q$$

Contestar

$$- 10q(3q+2)(q+4)$$

50. $$−5y^3−30y^2+35y$$

Trinomios Factoriales de la Forma $$ax^2+bx+c$$ usando el Método 'ac'

En los siguientes ejercicios, factor utilizando el método 'ac'.

51. $$5n^2+21n+4$$

Contestar

$$(5n+1)(n+4)$$

52. $$8w^2+25w+3$$

53. $$4k^2−16k+15$$

Contestar

$$(2k−3)(2k−5)$$

54. $$5s^2−9s+4$$

55. $$6y^2+y−15$$

Contestar

$$(3y+5)(2y−3)$$

56. $$6p^2+p−22$$

57. $$2n^2−27n−45$$

Contestar

$$(2n+3)(n−15)$$

58. $$12z^2−41z−11$$

59. $$60y^2+290y−50$$

Contestar

$$10(6y−1)(y+5)$$

60. $$6u^2−46u−16$$

61. $$48z^3−102z^2−45z$$

Contestar

$$3z(8z+3)(2z−5)$$

62. $$90n^3+42n^2−216n$$

63. $$16s^2+40s+24$$

Contestar

$$8(2s+3)(s+1)$$

64. $$24p^2+160p+96$$

65. $$48y^2+12y−36$$

Contestar

$$12(4y−3)(y+1)$$

66. $$30x^2+105x−60$$

Factor que usa la sustitución

En los siguientes ejercicios, factor usando sustitución.

67. $$x^4−x^2−12$$

Contestar

$$(x^2+3)(x^2−4)$$

68. $$x^4+2x^2−8$$

69. $$x^4−3x^2−28$$

Contestar

$$(x^2−7)(x^2+4)$$

70. $$x^4−13x^2−30$$

71. $$(x−3)^2−5(x−3)−36$$

Contestar

$$(x−12)(x+1)$$

72. $$(x−2)^2−3(x−2)−54$$

73. $$(3y−2)^2−(3y−2)−2$$

Contestar

$$(3y−4)(3y−1)$$

74. $$(5y−1)^2−3(5y−1)−18$$

Práctica Mixta

En los siguientes ejercicios, factor cada expresión utilizando cualquier método.

75. $$u^2−12u+36$$

Contestar

$$(u−6)(u−6)$$

76. $$x^2−14x−32$$

77. $$r^2−20rs+64s^2$$

Contestar

$$(r−4s)(r−16s)$$

78. $$q^2−29qr−96r^2$$

79. $$12y^2−29y+14$$

Contestar

$$(4y−7)(3y−2)$$

80. $$12x^2+36y−24z$$

81. $$6n^2+5n−4$$

Contestar

$$(2n−1)(3n+4)$$

82. $$3q^2+6q+2$$

83. $$13z^2+39z−26$$

Contestar

$$13(z^2+3z−2)$$

84. $$5r^2+25r+30$$

85. $$3p^2+21p$$

Contestar

$$3p(p+7)$$

86. $$7x^2−21x$$

87. $$6r^2+30r+36$$

Contestar

$$6(r+2)(r+3)$$

88. $$18m^2+15m+3$$

89. $$24n^2+20n+4$$

Contestar

$$4(2n+1)(3n+1)$$

90. $$4a^2+5a+2$$

91. $$x^4−4x^2−12$$

Contestar

$$(x^2+2)(x^2−6)$$

92. $$x^4−7x^2−8$$

93. $$(x+3)^2−9(x+3)−36$$

Contestar

$$(x−9)(x+6)$$

94. $$(x+2)^2−25(x+2)−54$$

## Ejercicios de escritura

95. Muchos trinomios del $$x^2+bx+c$$ factor de forma en el producto de dos binomios $$(x+m)(x+n)$$. Explica cómo encuentras los valores de $$m$$ y $$n$$.

Contestar

Las respuestas variarán.

96. Tommy factorizó $$x^2−x−20$$ como $$(x+5)(x−4)$$. Sara lo factorizó como $$(x+4)(x−5)$$. Ernesto lo factorizó como $$(x−5)(x−4)$$. ¿Quién está en lo correcto? Explica por qué los otros dos se equivocan.

97. Enumera, en orden, todos los pasos que das al usar el método “$$ac$$” para factorizar un trinomio de la forma $$ax^2+bx+c$$.

Contestar

Las respuestas variarán.

98. ¿En qué se asemeja el método “$$ac$$” al método “deshacer Foil”? ¿En qué es diferente?

## Autocomprobación

a. Después de completar los ejercicios, utilice esta lista de verificación para evaluar su dominio de los objetivos de esta sección.

b. Después de revisar esta lista de verificación, ¿qué hará para tener confianza en todos los objetivos?

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