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