x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
-2
y = x2 - 4x + 4 = (x - 2)2 has one repeated root
Limx→0 [ 1 / (x - 4) + 1 / (x + 4) ] / x = Limx→0 1 / (x2 - 4x) + 1 / (x2 + 4x) = Limx→0 (x2 + 4x) / (x4 - 16x2) + (x2 - 4x) / (x4 - 16x2) = Limx→0 (x2 + 4x - 4x + x2) / (x4 - 16x2) = Limx→0 2x2 / (x4 - 16x2) = Limx→0 2 / (x2 - 16) = 2 / (0 - 16) = -1/8
x2 - 4x = 8 x2 - 4x + 4 = 8 + 4 (x - 2)2 = 12 x - 2 = +&- sq. root of 12 x = 2 +&- 2(sq. root of 3)
6
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
-2
x2+4x+4 = 25 x2+4x+4-25 = 0 x2+4x-21 = 0 (x+7)(x-3) = 0 x = -7 or x = 3
x(x + 4)(x - 4) or x3 - 16x
x2 - 4
x2 - 4x - 32 = (x - 8)(x + 4)
x2 - 4x + 4 factors to (x - 2)(x - 2) or (x - 2)2
(x+2)6 (x2 + 4x + 4)(x+2)4 (x2 + 4x + 4)(x2 + 4x + 4)(x+2)2 (x2 + 4x + 4)(x2 + 4x + 4)(x2 + 4x + 4) (x4 + 4x3 + 4x2 + 4x3 + 16x2 + 16x + 4x2 + 16x + 16)(x2 + 4x + 4) (x4 + 8x3 + 24x2 + 32x + 16)(x2 + 4x + 4) (x6 + 4x5 + 4x4 + 8x5 + 32x4 + 32x3 + 24x4 + 96x3 + 96x2 + 32x3 + 128x2 +128x + 16x2 + 64x + 64) (x6 + 12x5 + 60x4 + 160x3 + 240x2 + 192x +64) the coefficeints are 1, 12, 60, 160, 240, and 192
x2 + 4x - 32 = (x + 8)*(x - 4)
x2 - 4x + 4 = 0 (x - 2)(x - 2) = 0 x = 2
x2+4x-32 = (x-4)(x+8) when factored