求x^4+2x^3+3x^2+2x+1分式因解

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求x^4+2x^3+3x^2+2x+1分式因解
求x^4+2x^3+3x^2+2x+1分式因解

求x^4+2x^3+3x^2+2x+1分式因解
x^4+x^2+2x^3++2x+x^2+1+x^2
=x^2(x^2+1)+2x(x^2+1)+(x^2+1)+x^2
=(x^2+2x+1)(x^2+1)+x^2
=(x^2+1)(x+1)^2+(x^2+1)-1
=(x^2+1)((x+1)^2+1)-1

x^4+2x^3+3x^2+2x+1=x^4+x^3+x^2+x^3+x^2+x+x^2+x+1=x^2(x^2+x+1)+x(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)^2

x^4+2x^3+3x^2+2x+1
=x^4+x^3+x^2+x^3+x^2+x+x^2+x+1
=x^2(x^2+x+1)+x(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)^2

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