(超急)關於equation+ function

1. 2x3 - x2 - 7x + 6 = 0

(2x3 - x2 - x) - (6x - 6) = 0

x(2x2 - x - 1) - 6(x - 1) = 0

x(2x + 1)(x - 1) - 6(x - 1) = 0

(x - 1)[x(2x + 1) - 6] = 0

(x - 1)(2x2 + x - 6) = 0

(x - 1)(x + 2)(2x - 3) = 0

x = 3/2, 1, -2


2. f(x) = 4x3 - 12x2 + 7x - 2

g(x) = 2x3 - 5x2 - 12x + 8

f(x) + g(x) = 6x3 - 17x2 - 5x + 6 = 0

(6x3 + x2 - 2x) - (18x2 + 3x - 6) = 0

x(6x2 + x - 2) - 3(6x2 + x - 2) = 0

(x - 3)(6x2 + x - 2) = 0

(x - 3)(2x - 1)(3x + 2) = 0

x = 3, 1/2, -2/3

Let f(x)= 2(x^3) - (x^2) - 7x + 6
f(1)= 0
so (x - 1) is the factor of f(x)

________2(x^2)_-_x-_8__________
x - 1 ) 2(x^3) - (x^2) - 7x + 6
_2(x^3) -2(x^2)________________
(x^2) - 7x
________(x^2)+_x______________
- 8x + 6
____________ - 8x + 8___________
- 2

2(x^2) -x -8+2
=(x - 2)(2x + 3)

x= -3/2 , 2 or 1