แบบฝึกหัด บท 2-3

ช่ือ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทักษะ 2.1 เร่ือง การแยกตัวประกอบของพหนุ ามท่มี ดี กี รสี ูงกวา่ สามที่สามารถจดั ใหอ้ ยู่ในรูปผลตา่ งของกำลงั สอง จงแยกตวั ประกอบของพหุนามต่อไปนี้ 1. 4x4 - 16x2 .................................................................................................................................................................... …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… .................................................................................................................................................................... …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. .................................................................................................................................................................... …………………………………………………………………………………………………………………………………………………… 2. 81y4 – 625 ................................................................................................................................................................... …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. .................................................................................................................................................................... …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. ................................................................................................................................................................... …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………..

ช่ือ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทักษะ 2.2 เร่อื ง การแยกตัวประกอบของพหุนามท่มี ดี ีกรสี งู กวา่ สามที่สามารถจัดใหอ้ ยู่ในรูปกำลงั สองสมบูรณ์ จงแยกตัวประกอบของพหนุ ามต่อไปนี้ 1. 25y4 + 120y2 + 144 …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… 2. x4 – 50x2 + 625 …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………………

ช่ือ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทกั ษะ 2.3 เร่ือง การแยกตัวประกอบของพหุนามทมี่ ีดกี รีสูงกว่าสามท่ีสามารถจัดให้อย่ใู นรปู ผลบวกหรือผลตา่ งของกำลังสาม จงแยกตวั ประกอบของพหนุ ามตอ่ ไปนี้ 1. x6 + 216 วิธีทำ…………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. 2. 216x6 - 27y6 วธิ ที ำ…………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………………….. 3. 192m3 + 3n3 …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. 4. x6 - 64 วธิ ีทำ …………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………….

ชื่อ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทักษะ 3.1 เรอื่ ง สมการกำลงั สองตวั แปรเดียว คำชแ้ี จง : ใหน้ ักเรยี นพจิ ารณา เพ่ือหาคำตอบ ตอนท่ี 1 ใหน้ ักเรียนพิจารณาหาคำตอบของสมการกำลังสองตัวแปรเดยี วต่อไปน้ี โดยวิธลี องแทนค่าตัวแปร 1) -10x + 24 = -x2 2) x2 + 9 = 0 ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... 3) x2 = -9 - 6x 4) 13x = -x2 - 30 ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ...............................................................

ชื่อ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทกั ษะ 3.2 เรือ่ ง ความหมายสมการกำลังสองตัวแปรเดียว ใหน้ กั เรยี นพิจารณาจำนวนทอ่ี ย่ใู นวงเลบ็ [ ] เป็นคำตอบของสมการหรือไม่ 1) x2 - x - 12 = 0 [-5 , 4] 2) x2 + 13x + 12 = 0 [-12 , -1] ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... 3) x2 + 2x - 35 = 0 [1 , 7] 4) 3x2 - 8x + 5 = 0 [1 , -1] ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ............................................................... ...............................................................

ช่ือ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทักษะ 3.3 เร่ือง การแก้สมการกำลงั สองตัวแปรเดียว โดยวิธกี ารแยกตวั ประกอบได้ จงแก้สมการต่อไปน้ี 1. จงแก้สมการ 5x2 + 7x – 6 = 0 ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. 2. จงแยกตัวประกอบของ 8x2 – 19x – 15 = 0 ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………….. 3. จงแยกตวั ประกอบของ 10x2 + 9x + 2 = 0 วิธที ำ …………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………………

ช่ือ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทกั ษะ 3.4 เรอื่ ง การแกส้ มการกำลังสองตัวแปรเดยี วที่เป็นผลตา่ งกำลงั สอง จงแกส้ มการตอ่ ไปน้ี 1. x2 - 64 = 0 ,,…………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………….. 2. (x – 21)2 - 100 = 0 ,,…………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………….. 3. (x –a)2 - (a +x)2 = 0 ,,…………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………………..

ช่ือ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทักษะ 3.5 เร่ือง การแกส้ มการกำลงั สองตัวแปรเดยี วโดยวธิ ีทำเปน็ กำลงั สองสมบรู ณ์ จงแก้สมการต่อไปน้ี 1. p2 + 49 = -14p วิธที ำ…………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………….. 2. u2 + 7u + 12 = 0 วธิ ีทำ ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………..

ชื่อ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทกั ษะ 3.6 เร่อื ง การแกส้ มการกำลังสองตวั แปรเดยี วโดยวธิ ีทำเป็นกำลังสองสมบูรณ์ จงแกส้ มการกำลังสองตัวแปรเดยี วตอ่ ไปนี้ 1. x2 + 4x - 1 = 0 วธิ ีทำ ……………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… 2. x2 + x - 30 = 0 วธิ ที ำ………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………. ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………..

ชื่อ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทกั ษะ 3.7 เรอ่ื ง การแกส้ มการกำลังสองตวั แปรเดยี วโดยใช้สูตร จงแกส้ มการกำลังสองตัวแปรเดียวโดยใช้สูตร 1. x2 + 26x + 165 = 0 วิธีทำ……………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………….. 2. 4y2 – 8y - 12 = 0 วิธีทำ……………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………….. …………………………………………………………………………………………………………………………………………

ชื่อ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทกั ษะ 3.8 เรอ่ื ง การแก้สมการกำลังสองตวั แปรเดยี วโดยใช้สตู ร จงแก้สมการต่อไปนี้ 1. 16x2 - 8x + 1 = 0 วิธีทำ ……………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… 2. 3z2 + 7z - 1 = 0 วิธีทำ………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………

ช่ือ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทักษะ 3.9 เรอ่ื ง การแก้สมการกำลังสองตวั แปรเดยี วโดยใช้สูตร จงแกส้ มการตอ่ ไปน้ี 1. 16x2 - 8x + 1 = 0 วธิ ีทำ ……………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… 2. 3z2 + 7z - 1 = 0 วิธที ำ………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………………..

ชื่อ……………………………………………..ช้นั ……เลขที่…. แบบฝึ กเสริมทักษะ 3.10 เร่อื ง โจทยป์ ัญหาเกย่ี วกบั สมการกำลังสองตวั แปรเดียว 1. ถา้ x, x + 7 และ x + 8 หน่วย เปน็ ความยาวของด้านทงั้ สามของรปู สามเหล่ียมมมุ ฉาก จงหาพ้นื ที่ของรูปสามเหลีย่ มมมุ ฉากรูปนี้ วธิ ีทำ …………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………….

ชื่อ……………………………………………..ช้นั ……เลขท่ี…. แบบฝึ กเสริมทักษะ 3.11 เร่อื ง โจทยป์ ัญหาสมการกำลงั สองตัวแปรเดียว 1. สนามรปู ส่เี หลี่ยมผนื ผา้ มคี วามกว้าง 35 เมตร และความยาว 52 เมตร ต้องการสรา้ งทางเดินรอบสนามใหม้ ีความกวา้ งเท่ากันท้ังสด่ี า้ น และพืน้ ทีข่ องทางเดนิ ท่ีสร้างเทา่ กับ 558 ตารางเมตร จงหาความกวา้ งของทางเดนิ รอบสนาม วิธีทำ …………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………. …………………………………………………………………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………