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การแยกตัวประกอบพหุนาม

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การแยกตัวประกอบพหุนาม

การแยกตัวประกอบของพหุนามดีกรีสอง
การแยกตัวประกอบของพหุนาม(Factoring  of  Polynomials) คือการเขียนพหุนามที่กำหนดให้ในรูปที่ง่ายกว่า พิจารณาการแยกตัวประกอบของพหุนามต่อไปนี้
5x-10  = 5(x-2)
5x-10    เป็นพหุนามดีกรีหนึ่ง
5           เป็นพหุนามดีกรีศูนย์
x-2        เป็นพหุนามดีกรีหนึ่ง
5(x-2)    เป็นรูปที่ง่ายกว่าของ 5x-10  โดยที่ 5 และ x-2   ต่างหาร 5x-10ลงตัวดังนั้น 5 และ x-2   จึงเป็นตัวประกอบ(factor)ของ 5x-10  
x2-3x-10 = (x+2) (x-5)
2x-3x-10     เป็นพหุนามดีกรีสอง
x-5             เป็นพหุนามดีกรีหนึ่ง
x+2            เป็นพหุนามดีกรีหนึ่ง
(x+2) (x-5)  เป็นรูปที่ง่ายกว่าของ x2-3x-10  โดยที่ x-5 และ x+2   ต่างหาร x2-3x-10  ลงตัวดังนั้น x-5 และ x+2   จึงเป็นตัวประกอบ(factor)ของ  x2-3x-10
สรุป   การแยกตัวประกอบพหุนามที่แต่ละพจน์มีสัมประสิทธิ์เป็นจำนวนเต็ม ทำได้โดย
1.ใช้สมบัติการแจกแจง โดยการนำ ห.ร.ม. ของค่าสัมบูรณ์ของสัมประสิทธิ์ของแต่ละพจน์ในพหุนามออกมาเป็นตัวประกอบของพหุนามที่กำหนดให้
2.เขียนพหุนามที่กำหนดให้ในรูปของการคูณกันของพหุนามที่มีดีกรีต่ำกว่า
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