x^(5)-3x^(2)+12x-1=a(x^(2))(x^(2)+x+1)(x^(2)+2)^(3)+Bx(x^(2)+x+1)(x^(2)+2)^(3)+c(x^(2)+x+1)(x^(2)+2)^(3)+(Dx+E)(x^(3))(x^(2)+2)+(Fx+G)x^(3)(x^(2)+x+1)(x^(2)+2)^(2)+(Hx+I)x^(3)(x^(2)+x+1)(x^(2)+2)+(Jx+K)x^(3)(x^(2)+x+1)
Are you looking for the values of x and also A through K? There are so many solutions. Perhaps infinite.