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Mathematics LibreTexts

1.1e: Exercises - Solve by Factoring

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    45462
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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. \(100y^4=9y^2   \\[4pt]\)

    Answers to Odd Exercises:

    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. \((x+4)(x-6) = 2(x+4)    \\[4pt] \)

    Answers to Odd Exercises:

    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. \((2y−3)(3y−1)=8y    \\[4pt]\)

    Answers to Odd Exercises:

    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. \(16x^2-40x+25 = 36    \\[4pt]\)

    Answers to Odd Exercises:

    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. \(x=10/3, \; x = -14/3 \)

    \( \bigstar \)


    1.1e: Exercises - Solve by Factoring is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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