คณิตพื้นฐาน ม.3 เทอม 1 เรื่อง 2 การแยกตัวประกอบของพหุนามที่มีดีกรีสูงกว่าสอง

เอกสารประกอบการสอนเอกสารประกอบการสอนวชิ าคณิตศาสตรพ2 น้ื ฐาน ม.3 เทอม 1 เร่อื ง การแยกตวั ประกอบของพหุนามทีม่ ดี ีกรสี ูงกว=าสอง 1
วิชาคณติ ศาสตรพ3 นื้ ฐาน

ม.3 เทอม 1

เร่อื ง การแยกตวั ประกอบของพหนุ ามท่ีมดี ีกรสี ูงกวา= สอง

ชโร่ือง เ…รยี …น………………………………………………………………………………………………ค…รผู …7ูส…อ…น………………ช…้นั ……………………………………….…เล…ข…ที่……………………..

เอกสารประกอบการสอนวชิ าคณติ ศาสตรพ2 น้ื ฐาน ม.3 เทอม 1 เร่ือง การแยกตัวประกอบของพหนุ ามทมี่ ดี ีกรีสูงกว=าสอง 2

แบบฝก< หัด 2.1 เรอ่ื ง การแยกตัวประกอบของพหุนามที่อยใHู นรูปผลบวก
และผลตHางของกำลงั สาม




จงแยกตัวประกอบของพหุนามต5อไปน ี้
1. x! + 27 2. y! + 64

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3. 8x! + 1 4. 64z! + 125

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5. 27x! + 512y! 6. 729 + (x − 2)!

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7. (3x − 1)! + (x − 4)!


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8. (2x + 5)! + (5x − 9)!

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9. x! − 1 10. z! − 216

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เอกสารประกอบการสอนวชิ าคณติ ศาสตรพ2 ้ืนฐาน ม.3 เทอม 1 เรือ่ ง การแยกตวั ประกอบของพหุนามที่มดี กี รีสูงกวา= สอง 3

11. 125y! − 64 12. 1,000 − 216x!

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13. 1,331y! − 343z!


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14. (4x + 3)! − 125

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15. 8 − (8x − 1)!

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16. (8x + 1)! + 8

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17. (5x − 2)! + (5x + 2)!

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เอกสารประกอบการสอนวชิ าคณิตศาสตรพ2 ้นื ฐาน ม.3 เทอม 1 เรือ่ ง การแยกตวั ประกอบของพหุนามทม่ี ดี ีกรสี ูงกวา= สอง 4

18. (2x + 5)! − (2x − 5)!

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19. (7x − 2)! − (6x + 9)!


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20. (8x − 15)! − (3x − 7)!

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21. x! − x" − x + 1


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22. y! + y" − 4y – 64

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เอกสารประกอบการสอนวชิ าคณติ ศาสตรพ2 ื้นฐาน ม.3 เทอม 1 เรอ่ื ง การแยกตวั ประกอบของพหนุ ามทีม่ ดี กี รสี งู กวา= สอง 5

แบบฝก< หัด 2.2 เรือ่ ง การแยกตัวประกอบของพหนุ ามที่มดี กี รีสงู กวาH สาม


จงแยกตวั ประกอบของพหุนามตอ5 ไปน ี้
1. x# + 3x" 2. 4x# − 16x"

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3. x$ − 81x# 4. x$ + 2x# + x"

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5. x# − 625 6. 81y# − 625

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7. 160,000x# − 10,000 8. x# − 50x" + 625

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9. 25y# + 120y" + 144 10. 77x# + 170x" + 77

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11. 77x# − 72x" − 77 12. x# − 10x" + 9

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13. x# − 29x" + 100 14. 64x$ − 729

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เอกสารประกอบการสอนวชิ าคณติ ศาสตรพ2 ้นื ฐาน ม.3 เทอม 1 เรอ่ื ง การแยกตวั ประกอบของพหนุ ามท่ีมีดกี รีสูงกวา= สอง 6

15. x$ + 216 16. 512 − y$

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………………………………………………………………............................……. 18. a$b! − 1

17. x# − y# ………………………………………………………………............................…….
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19. x$ − y$ ………………………………………………………………............................…….
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เอกสารประกอบการสอนวชิ าคณิตศาสตรพ2 น้ื ฐาน ม.3 เทอม 1 เร่ือง การแยกตัวประกอบของพหุนามทม่ี ดี กี รสี งู กวา= สอง 7

แบบฝ<กหัดทา7 ยบท เรื่อง การแยกตวั ประกอบของพหุนามทม่ี ีดีกรีสูงกวาH สอง


1. จงแยกตวั ประกอบของพหนุ ามตอ5 ไปน ้ี
1) 8 − x! 2) 27x! + 125


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4) 1,000 − (x + 10)!
3) (x − 3)! + 27


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5) (x − 11)! − (x + 11)!
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6) (x − 5)! − (7x + 4)!
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8) x# − 17x" + 16
7) 81x# − 2,401


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10) 10x# − x" − 3
9) x# − 32x" + 256


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เอกสารประกอบการสอนวิชาคณติ ศาสตรพ2 ้ืนฐาน ม.3 เทอม 1 เรอื่ ง การแยกตวั ประกอบของพหุนามท่มี ีดกี รีสงู กวา= สอง 8

11) 36x# − 97x" + 36

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12) y$ − 4,096

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13) 1 − a$

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14) 1,000,000z$ − 1

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15) x$ + 6x# + 9x" 16) 25x$ + 10x! + 1



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17) 81x# − 256y# 18) 64 − x!y!



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19) 343x$ + 1,000z$ 20) x$ − 4x!y + 4y"



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เอกสารประกอบการสอนวชิ าคณติ ศาสตรพ2 ืน้ ฐาน ม.3 เทอม 1 เร่อื ง การแยกตัวประกอบของพหนุ ามทีม่ ดี ีกรีสงู กว=าสอง 9

2. ถังนำ้ ทรงลกู บาศก? A มีความยาวภายในดEานละ x + 4 นว้ิ และถังนำ้ ทรงลูกบาศก? B มีความยาวภายใน
ดEานละ x − 2 นว้ิ ถงั น้ำท้ังสองมนี ำ้ บรรจอุ ยู5เตม็ อยากทราบว5า จะตEองใชถE งั น้ำ C ซึ่งมีความจุ x" + 2x + 28
ลกู บาศกน? ้วิ กใ่ี บ จึงจะใส5นำ้ ท้งั หมดจากถังน้ำ A และถงั นำ้ B ไดEพอดี
(เมือ่ x เปOนจำนวนเต็มบวกทมี่ ากกวา5 สอง)

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3. A, B และ C เปนO จำนวนเตม็ บวก ที่ B มากกว5า A และ C มากกวา5 B อย5เู ทา5 ๆ กนั
ถEาผลคณู ของทง้ั สามจำนวนเปนO x! + 12x" + 32x เม่ือ x เปOนจำนวนเตม็ บวก อยากทราบว5า

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1) B มากกวา5 A อยเ5ู ท5าใด
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2) ถาE ใหจE ำนวนทน่ี Eอยทส่ี ดุ ในสามจำนวนนี้ เทา5 กบั จำนวนเฉพาะสองหลกั ท่ีนEอยที่สดุ
ผลคณู และผลบวกของ A, B และ C จะเปOนเทา5 ไร

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เอกสารประกอบการสอนวชิ าคณติ ศาสตรพ2 ้นื ฐาน ม.3 เทอม 1 เรือ่ ง การแยกตวั ประกอบของพหนุ ามท่มี ีดกี รสี ูงกว=าสอง 10