Verified answer

(х^4+x^2+1)(x^4+x^2+2)-12=

=(x^8+2x^6+4x^4+3x^2+2)-12=

=x^8+2x^6+4x^4+3x^2-10=

=(x^8+2x^6)+(4x^4+3x^2-10)=

=(x^2+2)*x^6+(x^2+2)*(4x^2-5)=

=(x^2+2)(x^6+4x^2-5)=

=(x^6-x^5+x^5-x^4+x^4-x^3+x^3-x^2+5x^2-5x+5x-5)(x^2+2)=

=((x^6-x^5)+(x^5-x^4)+(x^4-x^3)+(x^3-x^2)+(5x^2-5x)+(5x-5))(x^2+2)=

=((x^5(x-1)+x^4(x-1)+x^3(x-1)+x^2(x-1)+5x(x-1)+5(x-1))(x^2+2)=

=(x-1)(x^5+x^4+x^3+x^2+5x+5)(x^2+2)=

=(x-1)((x^5+x^4)+(x^3+x^2+5x+5))(x^2+2)=

=(x-1)((x+1)x^4+(x+1)(x^2+5))(x^2+2)=

=(x-1)(x+1)(x^4+x^2+5)(x^2+2)

всего 4 множителя