# 多項式

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## 正式定義

${\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0}}$(降冪)

${\displaystyle a_{0}+a_{1}x+a_{2}x^{2}+...+a_{n-1}x^{n-1}+a_{n}x^{n}}$(升冪)

## 因式分解

• ${\displaystyle \ ab+ac=a(b+c)}$
• ${\displaystyle \ ac+ad+bc+bd=a(c+d)+b(c+d)=(a+b)(c+d)}$
• ${\displaystyle \ a^{2}-b^{2}=(a-b)(a+b)}$
• ${\displaystyle \ a^{2}+b^{2}=(a-ib)(a+ib)}$
• ${\displaystyle \ a^{2}+2ab+b^{2}=(a+b)^{2}}$
• ${\displaystyle \ a^{2}-2ab+b^{2}=(a-b)^{2}}$
• ${\displaystyle \ a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})}$
• ${\displaystyle \ a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})}$
• ${\displaystyle \ a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^{2}+...+ab^{n-2}+b^{n-1})}$