已知X平方+X+1=0,求X4次方+2X+4X+3X+2的值?

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已知X平方+X+1=0,求X4次方+2X+4X+3X+2的值?
已知X平方+X+1=0,求X4次方+2X+4X+3X+2的值?

已知X平方+X+1=0,求X4次方+2X+4X+3X+2的值?
x⁴+2x ³+4x²+3x+2
=x⁴+x³+x²+x³+x²+x+2x²+2x+2
=x²(x²+x+1)+x(x²+x+1)+2(x²+x+1)
=(x²+x+1)(x²+x+2)
=0×(x²+x+2)
=0

X^4+2X^3+4X^2+3X+2
=X^4+X^3+X^2+X^3+3X^2+3X+2
=X^2(X^2+X+1)+X^3+3X^2+3X+2
=X^3+3X^2+3X+2
=X^3+X^2+X+2X^2+2X+2
=X(X^2+X+1)+2X^2+2X+2
=2X^2+2X+2
=2(X^2+X+1)
=2*0
=0

X^4+2X^3+4X^2+3X+2
=X^4+X^3+X^2+X^3+3X^2+3X+2
=X^2(X^2+X+1)+X^3+3X^2+3X+2
=X^3+3X^2+3X+2
=X^3+X^2+X+2X^2+2X+2
=X(X^2+X+1)+2X^2+2X+2
=2X^2+2X+2
=2(X^2+X+1)
=2*0
=0
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