INneach of the following

1) 1- 8( x - 1)^3 = 0
(1-2x+2)(1+2(x-1)+4(x-1)^2)=0
(3-2x)(1+2x-2+4x^2-8x+1)=0
(3-2x)(4x^2-6x+2)=0
(3-2x)(4x-2)(x-1)=0
x=3/2 or x=1/2 or x=1


2.f (x) = x^4 - 2x^3 - 7x^2 + 8x + 12
=(x+1)(x^3-3x^2-4x+12)
=(x+1)(x-2)(x^2-x-6)
=(x-1)(x-2)(x-3)(x+2)


b) 0= x^4 - 2x^3 - 7x^2 + 8x + 12
0=(x-1)(x-2)(x-3)(x+2)

x=1 or x=2 or x=3 or x=-2

1.solve the equation 1- 8( x - 1)^3 = 0

1 - 8(x - 1)^3 = 0
8(x - 1)^3 = 1
(x - 1)^3 = 1/8
x - 1 = 1/2 since (1/2)^3 = 1/8
x = 3/2


2.
(a)
f(x) = x^4 - 2x^3 - 7x^2 + 8x + 12
f(x) = (x - 3)(x^3 + x^2 - 4x - 4) since f(3) = 0 , (x^3 + x^2 - 4x - 4) obtained
by 長除法
f(x) = (x - 3)(x - 2)(x^2 + 3x +2) since f(2) = 0 , (x^2 + 3x +2) obtained
by 長除法
f(x) = (x - 3)(x - 2)(x + 1)(x + 2)

(b)
f(x) = 0
(x - 3)(x - 2)(x + 1)(x + 2)=0
x = -2, x = -1, x = 2, x = 3

1.
1 - 8(x - 1)^3 = 0
8(x - 1)^3 = 1
(x - 1)^3 = 1/8
x - 1 = 1/2
x = 3/2


2.a)
f(x) = x^4 - 2x^3 - 7x^2 + 8x + 12
f(x) = (x - 3)(x^3 + x^2 - 4x - 4)
f(x) = (x - 3)(x - 2)(x^2 + 3x +2)
f(x) = (x - 3)(x - 2)(x + 1)(x + 2)

b)
f(x) = 0
x = 3, x = 2, x = -1, x = -2