x2+8x+4
Delta = 82-4x1x4 = 48 = 4 x sqrt(3)
so x2+8x+4= (x-((-8-sqrt(48))/2) (x-((-8+sqrt(48))/2) = (x+4+2 sqrt(3)) (x + 4 -2 sqrt(3))
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x + 4
x2 + 8x = x(x+8)
If you notice, 8x + 4 = 4(2x + 1), but there is an odd coefficient for x2, so there is guaranteed to be some remainder (that is 8x + 4 is not a factor of the polynomial): (24x3 - 5x2 - 48x - 8) ÷ (8x + 4) = 3x2 - 2x - 5 - (x2 - 12)/(8x + 4)
-6
(x - 4)(x - 4)