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A polynomial can be factored if it has a rational root.

If f(x) is a polynomial function of x and if there is a rational number p such that f(p) = 0 then

f(x) = (x-p)*g(x) where g(x) is a polynomial whose order is one less than the order of f(x).

If p = q/r where q and r are integers, then

(x - p) = (x - q/r) = (rx - q)/r which is a rational binomial factor. This does not work if p is irrational which is why p must be rational.

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