FACTORING QUARTIC POLYNOMIALS: A LOST ART

On the other hand, a quartic polynomial may factor into a product of two quadratic polynomials but have no roots in Q. For example, 1. 2 GARY BROOKFIELD f(x) = (x2 −2)(x2 −2) has no roots in Q but obviously factors. Thus to determine whether or not a quartic polynomial without rational ................
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