(1)x4-12x+323
=(x^4+36x^2+324)-(36x^2+12x+1)
=(x^2+18)^2-(6x+1)^2
=(x^2+6x+19)(x^2-6x+17)
(2) x4+7x3+14x2+7x+1
=(x^4+2x^2+1)+(7x^3+21x^2+7x)-9x^2
=(x^2+1)^2-(3x)^2+7x(x^2+3x+1)
=(x^2+3x+1)(x^2-3x+1)+7x(x^2+3x+1)
=(x^2+3x+1)(x^2+4x+1)