factorize polynomials

It seems that factor theorem is the only way to factorize it.
Let f(x) = 2x^3-5x^2-28x+15
Put x = 1/2
f(x) = 2(1/2)^3-5(1/2)^2-28(1/2)+15 = 0
(x-1/2), i.e. (2x-1) is a factor of f(x)
By long division,
we have, f(x) = (2x-1)(x^2-2x-15) = (2x-1)(x-5)(x+3)

2010-03-16 20:01:23 補充：
Let say,
Put x=0, f(x) = 15
Put x=1, f(x) = -16
From what I mention above, x should be in the range between 0 to 1.
And you may find the factor.....

This is my way to solve this kind of questions. I don't quite sure whether it is effective or not. Hope for other guys for better suggestions.