F4 1題Maths

x^6 + 2x^3 +1

= (x^3)^2 + 2x^3 + 1

= (x^3 + 1)^2

=[(x+1)(x^2 - x + 1)]^2



2010-01-24 20:55:40 補充：
f(x) = x^4 - 2x^3 - x^2 + 10x -8

= (x^2 - 3x + 4)(x^2 + x - 2)

g(x) = x^4 -3x^2 + 6x +8

= (x^2 - 3x + 4)(x^2 + 3x + 2)

Hence x^2 - 3x + 4 is a common factor of them.

2010-01-24 20:57:28 補充：
Let x^3 = a :

(x^3)^2 + 2x^3 + 1 = a^2 + 2a + 1 = (a + 1)^2

use (a + b)^2 = a^2 + 2ab + b^2) ,

a = x^3 and b = 1 here.