x的四次方+2x的三次方+3x的平方+2x+1

1.原式x^4+2x^3+3x^2+2x+1
=x^4+2x^2+1+2x^3+x^2+2x
=(x^2+1)^2+x^3+x+x^3+x^2+x
=(x^2+1)^2+x(x^2+1)+x(x^2+x+1)
=(x^2+1)(x^2+x+1)+x(x^2+x+1)
=(x^2+1+x)(x^2+1+x)
=(x^2+1+x)^2
2.
x^4+2x^3-9x^2-2x+8
=x^4+2x^3-x^2-2x+8-8x^2
=x^2(x^2-1)+2x(x^2-1)-8(x^2-1)
=(x^-1)(x^2+2x-8)
=(x+1)(x-1)(x+4)(x-2)