3x2 - 4x - 5 does not have rational factors.
Its roots are x = [4 +/- sqrt(76)]/6 ie -0.7863 and 2.11963 (approx).
So the factors are (x + 0.7863) and (x - 2.11963)
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x2 - 4x - 21 = (x-7)(x+3)
4x(4x^2 + 3x + 1)
2x(2x - 1)
(2x - 1)(4x + 1)
4(x - 1)(x + 1)