factor2

3)By remainder theoream ,If x-a is a factor of f(x) = x³ - x² + (2a-9)x - 9 , thenf(a) = 0a³ - a² + (2a-9)a - 9 = 0a³ + a² - 9a - 9 = 0a²(a + 1) - 9(a + 1) = 0(a + 1)(a² - 9) = 0(a + 1)(a - 3)(a + 3) = 0a = - 1 or a = 3 or a = - 3

Let f(x) = x^3 - x^2 + (2a - 9)x - 9
f(a) = 0
a^3 - a^2 + (2a - 9)a - 9 = 0
a^3 - a^2 + 2a^2 - 9a - 9 = 0
a^3 + a^2 - 9a - 9 = 0
Let g(a) = a^3 + a^2 - 9a - 9
g(3) = 3^3 + 3^2 - 9(3) - 9 = 0
So a - 3 is a factor of g(a)

2011-02-17 18:29:55 補充：
By long division,
g(a) = a^3 + a^2 - 9a - 9 = (a-3)(a^2+4a+3) = (a-3)(a+1)(a+3)
(a-3)(a+1)(a+3) = 0
a = 3 or a = -1 or a = -3