x^3-3px^2+(3p^2-q^2)x-p(p^2-q^2)
=x^3-3px^2+2xp^2+(p^2-q^2)x-p(p^2-q^2)
=x(x^2-3px+2p^2)+(p^2-q^2)(x-p)
=x(x-p)(x-2p)+(p^2-q^2)(x-p)
=(x-p)[x(x-2p)+(p^2-q^2)]
=(x-p)[x^2-2px+p^2-q^2]
=(x-p)[(x-p)^2-q^2]
=(x-p)(x-p+q)(x-p-q)
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