No, it has factors...
4x2 + 8x -21 = (2x+7)(2x-3)
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Not if x is an integer.
4x2 plus 3=11
4x2 + 12x + 5 = (2x + 1)(2x + 5).
8x3 + 4x2 + 6x + 3 = 4x2(2x + 1) + 3(2x + 1) = (2x + 1)(4x2 + 3)
x3 + 4x2 + 6x + 24 = (x2 + 6)(x + 4)