แบบฝึกหัด การแยกตัวประกอบของพหุนามดีกรีสอง

1. จงแยกตัวประกอบของพหุนามต่อไปนี้

  1. 2x2+5x+2
  2. 2x2+x6
  3. 3x213x+12
  4. 6x2+5x25
  5. 3x2x10
  6. 8x2+2x15
  7. 4x2+19x30
  8. 7x2+39x18
  9. 5x2+23x+12
  10. 9x2+9x40
  11. 6x2+19x+15
  12. 10x2+29x21
  13. 2x25x3
  14. 5x2+7x+6
  15. 2x27x15
  16. 6x2+13x+8
  17. 3x217x6
  18. 18x29x+2
  19. 6x2x40
  20. 16x2+66x27
  21. 7x25x2
  22. 28x2+31x5
  23. 8x26x9
  24. 12x229x+14
ดูเฉลยคำตอบ
  1. 2x2+5x+2=(2x+1)(x+2)
  2. 2x2+x6=(2x3)(x+2)
  3. 3x213x+12=(3x4)(x3)
  4. 6x2+5x25=(3x5)(2x+5)
  5. 3x2x10=(3x+5)(x2)
  6. 8x2+2x15=(4x5)(2x+3)
  7. 4x2+19x30=(4x5)(x+6)
  8. 7x2+39x18=(7x3)(x+6)
  9. 5x2+23x+12=(5x+3)(x+4)
  10. 9x2+9x40=(3x+8)(3x5)
  11. 6x2+19x+15=(3x+5)(2x+3)
  12. 10x2+29x21=(5x3)(2x+7)
  13. 2x25x3=(2x+1)(x3)
  14. 5x2+7x+6=(5x3)(x2)
  15. 2x27x15=(2x+3)(x5)
  16. 6x2+13x+8=(3x+8)(2x+1)
  17. 3x217x6=(3x+1)(x6)
  18. 18x29x+2=(6x1)(3x2)
  19. 6x2x40=(3x8)(2x+5)
  20. 16x2+66x27=(8x3)(2x+9)
  21. 7x25x2=(7x+2)(x1)
  22. 28x2+31x5=(7x1)(4x+5)
  23. 8x26x9=(4x+3)(2x3)
  24. 12x229x+14=(3x2)(4x7)

2. จงแยกตัวประกอบของพหุนามต่อไปนี้ โดยวิธีทำเป็นกำลังสองสมบูรณ์

  1. x2+8x84
  2. x28x+15
  3. x2+8x+15
  4. x224x+143
  5. x22x8
  6. x2+10x7
  7. x27x1
  8. x2+5x3
  9. 2x2+3x+1
  10. 2x2+x3
ดูเฉลยคำตอบ
  1. x2+8x84
    =x2+2(4)x+(4)2(4)284=(x+4)21684=(x+4)2102=(x+4+10)(x+410)=(x+14)(x6)
  2. x28x+15
    =x22(4)x+(4)2(4)2+15=(x4)216+15=(x4)2(1)2=(x4+1)(x41)=(x3)(x5)
  3. x2+8x+15
    =x2+2(4)x+(4)2(4)2+15=(x+4)216+15=(x+4)2(1)2=(x+4+1)(x+41)=(x+5)(x+3)
  4. x224x+143
    =x22(12)x+(12)2(12)2+143=(x12)2144+143=(x12)2(1)2=(x12+1)(x121)=(x11)(x13)
  5. x22x8
    =x22(1)x+(1)2(1)28=(x1)218=(x1)2(3)2=(x1+3)(x13)=(x+2)(x4)
  6. x2+10x7
    =x2+2(5)x+(5)2(5)27=(x+5)2257=(x+5)2(32)2=(x+5)2(42)2=(x+5+42)(x+542)
  7. x27x1
    =x22(72)x+(72)2(72)21=(x72)24941=(x72)2534=(x72)2(532)2=(x7+532)(x7532)
  8. x2+5x3
    =x2+2(52)x+(52)2(52)23=(x+52)22543=(x+52)2374=(x+52)2(372)2=(x+5+372)(x+5372)
  9. 2x2+3x+1
    =2[x2+32x+12]=2[x2+2(34)x+(34)2(34)2+12]=2[(x+34)2916+12]=2[(x+34)2116]=2[(x+34)2(14)2]=2[(x+34+14)(x+3414)]=2[(x+1)(x+12)]
  10. 2x2+x3
    =2[x2+12x32]=2[x2+2(14)x+(14)2(14)232]=2[(x+14)211632]=2[(x+14)22516]=2[(x+14)2(54)2]=2[(x+14+54)(x+1454)]=2[(x+32)(x1)]

3. การแยกตัวประกอบรวมทุกแบบ (โจทย์ระคน)

  1. 6a2+9a
  2. 5a410a2
  3. a24
  4. x3x
  5. x21
  6. a3+2a2
  7. b2100
  8. a2b2
  9. x2x
  10. 2x2+6x2
  11. 9c216d2
  12. c225
  13. c25c
  14. m24n2
  15. a2b29
  16. 2a2+a
  17. 4a3a
  18. a3b3
  19. a22ab+b2
  20. a2+ab
  21. c216
  22. c28c+16
  23. 3c9
  24. x2+3x+2
  25. x27x+6
  26. x24x12
  27. x2+4x
  28. x39x
  29. x2+2x8
  30. x2+x6
  31. x2+7x+12
  32. x2+9x+20
  33. x2+3x+2
  34. x2+5x+6
  35. x3+9x2+20x
  36. x2+5x+4
  37. x2+7x+10
  38. x2+3x+2
  39. y22y24
  40. y2y12
  41. y2+6y+9
  42. a24a21
  43. a3+27
  44. m2m12
  45. m364
  46. m2+m6
  47. 2yy26y3
  48. 27y+6y2
  49. 4y+12y2+9y3
  50. 49y2
  51. b427b
  52. 4b225
  53. 2b2+5b
  54. 2b211b+5
  55. 3x27x+2
ดูเฉลยคำตอบ
  1. 6a2+9a=3a(2a+3)
  2. 5a410a2=5a2(a22)
  3. a24=(a2)(a+2)
  4. x3x=x(x21)=x(x1)(x+1)
  5. x21=(x1)(x+1)
  6. a3+2a2=a2(a+2)
  7. b2100=b2102=(b10)(b+10)
  8. a2b2=(ab)(a+b)
  9. x2x=x(x1)
  10. 2x2+6x2=8x2
  11. 9c216d2=(3c4d)(3c+4d)
  12. c225=(c5)(c+5)
  13. c25c=c(c5)
  14. m24n2=(m2n)(m+2n)
  15. a2b29=(ab3)(ab+3)
  16. 2a2+a=a(2a+1)
  17. 4a3a=a(4a21)
  18. a3b3=(ab)(a2+ab+b2)
  19. a22ab+b2=(ab)2
  20. a2+ab=a(a+b)
  21. c216=(c4)(c+4)
  22. c28c+16=(c4)2
  23. 3c9=3(c3)
  24. x2+3x+2=(x+1)(x+2)
  25. x27x+6=(x6)(x1)
  26. x24x12=(x6)(x+2)
  27. x2+4x=x(x+4)
  28. x39x=x(x29)=x(x3)(x+3)
  29. x2+2x8=(x2)(x+4)
  30. x2+x6=(x2)(x+3)
  31. x2+7x+12=(x+3)(x+4)
  32. x2+9x+20=(x+4)(x+5)
  33. x2+3x+2=(x+2)(x+1)
  34. x2+5x+6=(x+3)(x+2)
  35. x3+9x2+20x=x(x2+9x+20)=(x)(x+4)(x+5)
  36. x2+5x+4=(x+4)(x+1)
  37. x2+7x+10=(x+5)(x+2)
  38. x2+3x+2=(x+2)(x+1)
  39. y22y24=(y6)(y+4)
  40. y2y12=(y4)(y+3)
  41. y2+6y+9=(y+3)(y+3)=(y+3)2
  42. a24a21=(a7)(a+3)
  43. a3+27=a3+33=(a+3)(a23a+9)
  44. m2m12=(m4)(m+3)
  45. m364=m343=(m4)(m2+4m+16)
  46. m2+m6=(m2)(m+3)
  47. 2yy26y3=(y)(6y2+y2)=(y)(2y1)(3y+2)
  48. 27y+6y2=6y27y+2=(3y2)(2y1)
  49. 4y+12y2+9y3=y(9y2+12y+4)=(y)(3y+2)(3y+2)=(y)(3y+2)2
  50. 49y2=(23y)(2+3y)
  51. b427b=b(b327)=b(b3)(b2+3b+9)
  52. 4b225=(2b)252=(2b5)(2b+5)
  53. 2b2+5b=b(2b+5)
  54. 2b211b+5=(2b1)(b5)
  55. 3x27x+2=(3x1)(x2)

Leave a Reply

Thumbnails managed by ThumbPress