中五數學~~續多項式的因式定理及其應用,要列過程.

1.(a)
P(x)
= x³ + 3x² - x - 3
= (x³ + 3x²) - (x + 3)
= x²(x + 3) - (x + 3)
= (x + 3)(x² - 1)
= (x + 3)(x + 1)(x - 1)

1.(b)
P(x) = 0
(x + 3)(x + 1)(x - 1) = 0
x + 3 = 0 或 x + 1 = 0 或 x - 1 = 0
x = -3 或 x = -1 或 x = 1


2.(a)
公式：(u - v)³ = u³ - 3u²v + 3uv² - v³

Q(x)
= x³ - 3x² + 3x - 1
= x³ - 3x²(1) + 3x(1)² - (1)³
= (x - 1)³

2.(b)
Q(x) = 0
(x - 1)³ = 0
x = 1 (三根)

圖片參考：http://img715.imageshack.us/img715/1189/screenhunter02sep212326.gif


http://img715.imageshack.us/img715/1189/screenhunter02sep212326.gif