作业帮因式分解：x的8次方+x+1
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因式分解：x的8次方+x+1
因式分解：x的8次方+x+1
因式分解：x的8次方+x+1
x8+x7+x6-x7-x6-x5+x5+x4+x3-x4-x3-x2+x2+x+1,每3项合并即可（x²+x+1）
x^8+x+1
=(x^8-x^2)+(x^2+x+1)
=x^2(x^6-1)+(x^2+x+1)
=x^2(x^3-1)(x^3+1)+(x^2+x+1)
=x^2(x-1)(x^2+x+1)(x^3+1)+(x^2+x+1)
=(x^2+x+1)(x^6-x^5+x^3-x^2)+(x^2+x+1)
=(x^2+x+1)(x^6-x^5+x^3-x^2+1)
x的8次方+x+1
=X^8+X+1
=X^8+X^7-X^7+X^6-X^6+X^5-X^5+X^4-X^4+X^3-X^3+X^2-X^2+X+1
= (X^8+X^7+X^6) -(X^7+X^6+X^5)+(X^5+X^4+X^3)-(X^4+X^3+X^2)+(X^2+X+1)
= X^6(X^2+X+1)-X^5(X^2+X+1)+X^3(X^2+X+1)-X^2(X^2+X+1)+(X^2+X+1)
= (X^2+X+1)( X^6-X^5+X^3-X^2+1)
X^8+X+1
=(X^4+1)(X^4-1)+X+2
=[(X^2+1)(X^2-1)+2](X^2+1)(X^2-1)+X+2
=[(X^2+1)(X^2-1)]^2+2(X^2+1)(X^2-1)+X+2
=[(X^2+1)(X^2-1)+1]^2+X+1
={[(X+1)(X-1)+2](X+1)(X-1)+1}^2+X+1
=[(X+1)(...
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X^8+X+1
=(X^4+1)(X^4-1)+X+2
=[(X^2+1)(X^2-1)+2](X^2+1)(X^2-1)+X+2
=[(X^2+1)(X^2-1)]^2+2(X^2+1)(X^2-1)+X+2
=[(X^2+1)(X^2-1)+1]^2+X+1
={[(X+1)(X-1)+2](X+1)(X-1)+1}^2+X+1
=[(X+1)(X-1)^2+2(X+1)(X-1)+1]^2+X+1
={[(X+1)(X-1)+1]^2}^2+X+1
=[(X+1)(X-1)+1]^4+X+1
X^8+X+1
=(X^2)^4+X+1
=[(X+1)(X-1)+1]^4+X+1
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