# 1.1e: Exercises - Solve by Factoring

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### A: Solve by Factoring

Exercise $$\PageIndex{A}$$

Solve by factoring (Zero Factor Property, GCF, Difference of Squares).

 1. $$(3a−10)(2a−7)=0 \\[4pt]$$ 2. $$(5b+1)(6b+1)=0 \\[4pt]$$ 3. $$6m(12m−5)=0 \\[4pt]$$ 4. $$2x(6x−3)=0 \\[4pt]$$ 5. $$(2x−1)^2=0 \\[4pt]$$ 6. $$(3y+5)^2=0 \\[4pt]$$ 7. $$8( 2 x + 1 ) ( 3 x - 5 ) = 0 \\[4pt]$$ 8. $$4 (5 x - 1 ) ( 2 x + 3 ) = 0 \\[4pt]$$ 9. $$x^2 + 4x = 0 \\[4pt]$$ 10. $$3x^2 + 2x = 0 \\[4pt]$$ 11.  $$4x^3 = 36 x^2 \\[4pt]$$ 12. $$16 x^2 = 8x \\[4pt]$$ 13. $$7a^2+14a=7a \\[4pt]$$ 14. $$2x^2 - 25x = 7x^2 \\[4pt]$$ 15. $$49m^2=144 \\[4pt]$$ 16. $$625=x^2 \\[4pt]$$ 17. $$16y^2=81 \\[4pt]$$ 16. $$64p^2=225\\[4pt]$$ 19. $$121n^4=36n^2 \\[4pt]$$ 20. $$100y^4=9y^2 \\[4pt]$$
 1. $$a=\frac{10}{3},\; a=\frac{7}{2}$$ 3. $$m=0,\; m=\frac{5}{12}$$ 5. $$x=\frac{1}{2}$$ 7. $$x=- \frac { 1 } { 2 } ,\; x=\frac { 5 } { 3 }$$ 9. $$x = 0 , \; x =-4$$ 11.  $$x = 0,\; x=9$$ 13. $$a=−1,\; a=0$$ 15. $$m=\frac{12}{7},\; m=−\frac{12}{7}$$ 17. $$y=−\frac{9}{4},\; y=\frac{9}{4}$$ 19. $$n=0, \; n=−\frac{6}{11},\; n=\frac{6}{11}$$

$$\bigstar$$

Solve each trinomial equation by factoring.

 21. $$x ^ { 4 } - 5 x ^ { 2 } + 4 = 0 \\[4pt]$$ 22. $$4 x ^ { 4 } - 37 x ^ { 2 } + 9 = 0 \\[4pt]$$ 23. $$x ^ { 2 } - 15 x + 50 = 0 \\[4pt]$$ 24. $$x ^ { 2 } + 10 x - 24 = 0 \\[4pt]$$ 25. $$x^2+36 = 13x \\[4pt]$$ 26. $$n^2=5−6n \\[4pt]$$ 27. $$3y^2−18y=−27 \\[4pt]$$ 28. $$4x^2 + 100 = 40x \\[4pt]$$ 29. $$x^3+36x=12x^2 \\[4pt]$$ 30. $$m^3−2m^2=−m \\[4pt]$$ 31. $$3y^3+48y=24y^2 \\[4pt]$$ 32. $$2y^3+2y^2=12y \\[4pt]$$ 33. $$(x+6)(x−3)=−8 \\[4pt]$$ 34. $$(p−5)(p+3)=−7 \\[4pt]$$ 35. $$( x + 4 ) ( x - 2 ) = 16 \\[4pt]$$ 36. $$( x + 1 ) ( x - 7 ) = 9 \\[4pt]$$ 37. $$(x+1)(x−3)=−4x \\[4pt]$$ 38. $$(y−3)(y+2)=4y \\[4pt]$$ 39. $$( x + 2 ) ( x - 8 ) = 2(x - 14 )\\[4pt]$$ 40. $$(x+4)(x-6) = 2(x+4) \\[4pt]$$
 21. $$x=\pm 1 ,\; x= \pm 2$$ 23. $$x=5, \; x=10$$ 25. $$a=4,\; a=9$$ 27. $$y = 3$$ 29. $$x=0 \; x=6$$ 31. $$x=0,\space x=4$$ 33. $$x=2,\; x=−5$$ 35. $$x=- 6, \; x=4$$ 37. $$x=1,\; x=−3$$ 39. $$x=2, \; x=6$$

$$\bigstar$$

Solve each trinomial equation by factoring.

 41. $$3 x ^ { 2 } + 2 x - 5 = 0 \\[4pt]$$ 42. $$2 x ^ { 2 } + 9 x + 7 = 0 \\[4pt]$$ 43. $$5a^2−26a=24 \\[4pt]$$ 44. $$4b^2+7b=−3 \\[4pt]$$ 45. $$4m^2=17m−15 \\[4pt]$$ 46. $$4x^2−13x=−3 \\[4pt]$$ 47. $$20x^2−60x=−45 \\[4pt]$$ 48. $$18b^2+60b+50=0 \\[4pt]$$ 49. $$15x^2−10x=40 \\[4pt]$$ 50. $$14y^2−77y=−35 \\[4pt]$$ 51. $$18x^2−9=−21x \\[4pt]$$ 52. $$16y^2+12=−32y \\[4pt]$$ 53. $$6 x ^ { 2 } - 5 x - 2 = 30 x + 4 \\[4pt]$$ 54. $$6 x ^ { 2 } - 9 x + 15 = 20 x - 13 \\[4pt]$$ 55. $$5x^2 - 39x + 12 = 4(x -3) \\[4pt]$$ 56. $$4 x ^ { 2 } + 5 x - 5 = 15 ( 3 - 2 x ) \\[4pt]$$ 57. $$( 6 x + 1 ) ( x + 1 ) = 6 \\[4pt]$$ 58. $$( 2 x - 1 ) ( x - 4 ) = 39 \\[4pt]$$ 59. $$(3x−2)(x+4)=12x \\[4pt]$$ 60. $$(2y−3)(3y−1)=8y \\[4pt]$$
 41. $$x=- \frac { 5 } { 3 } , \; x= 1$$ 43. $$a=−\frac{4}{5},\; a=6$$ 45. $$m=\frac{5}{4},\; m=3$$ 47. $$x=\frac{3}{2}$$ 49. $$x=2,\; x=−\frac{4}{3}$$ 51. $$x=−\frac{3}{2},\; x=\frac{1}{3}$$ 53. $$x=- \frac { 1 } { 6 } , \; x=6$$ 55. $$x=\frac { 3 } { 5 } , \; x=8$$ 57. $$x=- \frac { 5 } { 3 } , \; x=\frac { 1 } { 2 }$$ 59. $$x=- \frac { 4 } { 3 } , \; x=2$$

$$\bigstar$$

Solve each polynomial equation by factoring.

 61. $$4 x ^ { 3 } - 14 x ^ { 2 } - 30 x = 0 \\[4pt]$$ 62. $$9 x ^ { 3 } + 48 x ^ { 2 } - 36 x = 0 \\[4pt]$$ 63. $$- 10 x ^ { 3 } - 28 x ^ { 2 } + 48 x = 0 \\[4pt]$$ 64. $$- 2 x ^ { 3 } + 15 x ^ { 2 } + 50 x = 0 \\[4pt]$$ 65. $$16p^3=24p^2-9p \\[4pt]$$ 66. $$36x^3+24x^2=−4x \\[4pt]$$ 67. $$\dfrac { 1 } { 10 } x ^ { 2 } - \dfrac { 7 } { 15 } x - \dfrac { 1 } { 6 } = 0 \\[4pt]$$ 68. $$\dfrac { 2 } { 3} x ^2 - \dfrac { 7 } { 3} x - \dfrac { 5 } {4 } = 0 \\[4pt]$$ 69. $$\dfrac { 1 } { 4 } - \dfrac { 4 } { 9 } x ^ { 2 } = 0 \\[4pt]$$ 70. $$\dfrac { 2 } {25 } x ^ { 2 } = \dfrac { 1 } {2 } \\[4pt]$$ 71. $$\dfrac { 1 } { 3 } x ^ { 3 } - \dfrac { 3 } { 4 } x = 0 \\[4pt]$$ 72. $$\dfrac { 1 } { 2 } x ^ { 3 } - \dfrac { 1 } { 50 } x = 0 \\[4pt]$$ 73. $$2 x ^ { 3 } - x ^ { 2 } - 72 x + 36 = 0 \\[4pt]$$ 74. $$x ^ { 3 } - 3 x ^ { 2 } - x + 3 = 0 \\[4pt]$$ 75. $$45 x ^ { 3 } - 9 x ^ { 2 } - 5 x + 1 = 0 \\[4pt]$$  76. $$4 x ^ { 3 } - 32 x ^ { 2 } - 9 x + 72 = 0 \\[4pt]$$ 77. $$16x^2 +24x +9 = 144x^2 \\[4pt]$$ 78. $$25x^2 - 80x + 64 = 100x^2 \\[4pt]$$ 79. $$9x^2 +12x +4 = 144 \\[4pt]$$ 80. $$16x^2-40x+25 = 36 \\[4pt]$$
 61. $$x=0 , \; x=- \frac { 3 } { 2 } , \; x=5$$ 63. $$x=- 4, \;x=0 , \; x=\frac { 6 } { 5 }$$ 65. $$p=0,\; p=\frac{3}{4}$$ 67. $$x=-\frac { 1 } { 3 } , \; x=5$$ 69. $$x = \pm \frac{3}{4}$$ 71. $$x=0 ,\; x= \pm \frac { 3 } { 2 }$$ 73. $$x=\pm 6 ,\; x= \frac { 1 } { 2 }$$ 75. $$x=\pm \frac { 1 } { 3 } , \;x= \frac { 1 } { 5 }$$ 77. $$x=3/8, \; x=-3/16$$ 79. $$x=10/3, \; x = -14/3$$
$$\bigstar$$