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)
x + 4
(x-4)(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)
If that's + 4x2, the answer is 2x(x2 + 2x - 4)
-6
(x - 4)(x - 4)
That does not factor neatly.
x2 + 8x + 15 = (x + 3)(x + 5)
x2-8x+15 = (x-3)(x-5)
x2 + 8x + 15 = (x + 3) (x + 5).
x2 - 8x = 1 ∴ x2 - 8x + 16 = 17 ∴ (x - 4)2 = 17 ∴ x - 4 = ±√17 ∴ x = 4 ± √17