分解因式 1；x的4次方+x的平方+1 2；x的3次方+6x的平方+11x+6 3; a的平方+2b的平方+3c的平方+

x^4+x^2+1
=(x^4+2x^2+1)- x^2
=(x^2+1)^2-x^2
=(x^2+x+1)(x^2-x+1)
x^3-6x^2+11x+6
=x^3-6x^2+9x+2x+6
=x(x^2-6x+9)+2(x+3)
=x(x-3)^2+2(x+3)
=(x+3)(x^2+3x+2)
=(x+3)(x+2)(x+1)
a^2+2b^2+3c^2+4ac+5bc+3ab
=(a^2+3ab+2b^2)+4ac+5bc+3c^2
=(a+2b)(a+b)+(4a+5b)c+3c^2
=(a+2b)(a+b)+3(a+b)c+(a+2b)c+3c^2
=(a+2b+3c)(a+b+c)

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