Polynomials

Consider f(x)=x^3+x^2-4x-4
(a) Find the value of f(-1)
(b) Factorize f(x)
(c) If f(x)=(x-1) g(x) + r where r is a constant, find g(x) and r.

(a)
f(-1)
=(-1)^3+(-1)^2-4(-1)-4
=0
(b)
f(x)
=(x+1)(x^2-4)
=(x+1)(x-2)(x+2)
(c)
f(1)
=1+1-4-4
=-6
f(x)-r=(x-1) g(x)
x^3+x^2-4x-4+6=(x-1)g(x)
x^3+x^2-4x+2=(x-1)g(x)
x^3+x^2-4x+2=(x-1)(x^2+2x-2)
g(x)=x^2+2x-2

2007-02-12 19:34:18 補充：
r=f(1) 用remainder theorem